Free Printable Unit 9: Conic Sections

1.

Directions: Write the equation of each circle with the given information. Center: (-9, 0), Radius: 1

a)

$(x + 9)^2 + y^2 = 1$

b)

$(x - 9)^2 + y^2 = 1$

c)

$(x + 9)^2 + (y - 1)^2 = 1$

d)

$(x - 9)^2 + (y + 1)^2 = 1$

2.

Directions: Write the equation of each circle with the given information. Center: (3, -3), Radius: 2√6

a)

$(x - 3)^2 + (y + 3)^2 = 24$

b)

$(x + 3)^2 + (y - 3)^2 = 24$

c)

$(x - 3)^2 + (y - 3)^2 = 24$

d)

$(x + 3)^2 + (y + 3)^2 = 24$

3.

Directions: Write the equation of each circle with the given information. Center: (4, 7), Endpoint: (-1, -2)

a)

$(x - 4)^2 + (y - 7)^2 = 106$

b)

$(x + 4)^2 + (y + 7)^2 = 106$

c)

$(x - 4)^2 + (y - 7)^2 = 81$

d)

$(x + 4)^2 + (y + 7)^2 = 81$

4.

Directions: Write the equation of each circle with the given information. Center: (0, -8), Endpoint: (2, -5)

a)

$(x - 0)^2 + (y + 8)^2 = 13$

b)

$(x + 0)^2 + (y - 8)^2 = 13$

c)

$(x - 0)^2 + (y + 8)^2 = 9$

d)

$(x + 0)^2 + (y - 8)^2 = 9$

5.

Directions: Write the equation of each circle with the given information. Endpoints of Diameter: (-6, 2) and (-8, 10)

a)

$(x + 7)^2 + (y - 6)^2 = 17$

b)

$(x + 7)^2 + (y - 6)^2 = 34$

c)

$(x + 7)^2 + (y - 6)^2 = 68$

d)

$(x + 7)^2 + (y - 6)^2 = 136$

6.

Directions: Write the equation of each circle with the given information. Endpoints of Diameter: (-13, -7) and (11, 11)

a)

$(x + 1)^2 + (y - 3)^2 = 169$

b)

$(x - 1)^2 + (y + 3)^2 = 169$

c)

$(x - 1)^2 + (y - 2)^2 = 169$

d)

$(x + 1)^2 + (y + 2)^2 = 169$

7.

Directions: Write the equation of each circle with the given information. (Image of a circle on a grid)

a)

$x^2 + y^2 = r^2$

b)

$(x - h)^2 + (y - k)^2 = r^2$

c)

$x^2 + y^2 + 2gx + 2fy + c = 0$

d)

$(x - a)^2 + (y - b)^2 = r^2$

8.

Directions: Determine the standard form equation of a circle given the center and radius. (Image of a circle with center and radius marked)

a)

$x^2 + y^2 = r^2$

b)

$(x - h)^2 + (y - k)^2 = r^2$

c)

$x^2 + y^2 + 2gx + 2fy + c = 0$

d)

$(x - a)^2 + (y - b)^2 = r^2$

9.

Identify the center and radius of each circle given the equations below. $(x + 1)^2 + (y + 4)^2 = 81$ .

a)

Center: (-1, -4), Radius: 9

b)

Center: (1, 4), Radius: 81

c)

Center: (-1, 4), Radius: 9

d)

Center: (1, -4), Radius: 9

10.

Identify the center and radius of each circle given the equations below. $x^2 + (y - 5)^2 = 7$ .

a)

Center: (0, 5), Radius: √7

b)

Center: (0, -5), Radius: 7

c)

Center: (5, 0), Radius: √7

d)

Center: (0, 5), Radius: 7

11.

11. $(x - 7)^2 + (y + 2)^2 = 40$ . Identify the center and radius of the circle. Center: _______ Radius: _______

a)

Center: (7, -2), Radius: 6.32

b)

Center: (7, -2), Radius: 40

c)

Center: (-7, 2), Radius: 6.32

d)

Center: (-7, 2), Radius: 40

12.

12. $2(x + 6)^2 + 2y^2 = 144$ . Identify the center and radius of the circle. Center: _______ Radius: _______

a)

Center: (-6, 0), Radius: 6

b)

Center: (6, 0), Radius: 12

c)

Center: (-6, 0), Radius: 12

d)

Center: (0, 6), Radius: 6

13.

Directions: Write the equation in standard form, identify the center and radius, then graph the circle. 13. $3x^2 + 3y^2 - 5 = 0$ Center: _______ Radius: _______

a)

Center: (0, 0), Radius: 3

b)

Center: (0, 0), Radius: 5

c)

Center: (0, 0), Radius: 7

d)

Center: (0, 0), Radius: 10

14.

Directions: Write the equation in standard form, identify the center and radius, then graph the circle. 14. $x^2 + y^2 + 13y = y - 32$ . Center: _______ Radius: _______

a)

Center: (0, -7), Radius: 9

b)

Center: (0, 7), Radius: 9

c)

Center: (0, -7), Radius: 5

d)

Center: (0, 7), Radius: 5

15.

Directions: Write the equation in standard form, identify the center and radius, then graph the circle. 15. $x^2 + y^2 + 7y = 10x - 3y - 13$ Center: _______ Radius: _______

a)

Center: (5, -2.5), Radius: 7.5

b)

Center: (5, -3.5), Radius: 8.5

c)

Center: (5, -3.5), Radius: 7.5

d)

Center: (5, -2.5), Radius: 8.5

16.

Directions: Identify the center of the ellipse given by the equation $\frac{x^2}{64} + \frac{y^2}{9} = 1$ . What is the center of the ellipse?

a)

(0, 0)

b)

(8, 0)

c)

(0, 3)

d)

(8, 3)

17.

Directions: Graph each ellipse. Identify the center, vertices, co-vertices, and foci. 2. $\frac{x^2}{36} + \frac{y^2}{1} = 1$ What is the center of the ellipse?

a)

(0, 0)

b)

(1, 0)

c)

(0, 1)

d)

(1, 1)

18.

Directions: Identify the center of the ellipse given by the equation $\frac{x^2}{16} + \frac{y^2}{7} = 1$ . What is the center of the ellipse?

a)

(0, 0)

b)

(1, 1)

c)

(4, 0)

d)

(0, 4)

19.

Directions: Graph each ellipse. Identify the center, vertices, co-vertices, and foci. 4. $\frac{(x+1)^2}{25} + \frac{(y+1)^2}{49} = 1$ What is the center of the ellipse?

a)

(-1, -1)

b)

(1, 1)

c)

(0, 0)

d)

(1, -1)

20.

Graph the equation $\frac{(x+3)^2}{45} + \frac{(y-1)^2}{81} = 1$ on the provided grid. Fill in the following: Center: __________, Vertices: __________, Co-Vertices: __________, Foci: __________.

a)

Center: (-3, 1), Vertices: (-3, 10) and (-3, -8), Co-Vertices: (3√5, 1) and (-9, 1), Foci: (-3, 1+√36) and (-3, 1-√36).

b)

Center: (3, -1), Vertices: (3, 10) and (3, -8), Co-Vertices: (3√5, -1) and (-9, -1), Foci: (3, -1+√36) and (3, -1-√36).

c)

Center: (-3, 1), Vertices: (-3, 9) and (-3, -7), Co-Vertices: (3√5, 1) and (-9, 1), Foci: (-3, 1+√45) and (-3, 1-√45).

d)

Center: (-3, 1), Vertices: (-3, 10) and (-3, -8), Co-Vertices: (3√5, 1) and (-9, 1), Foci: (-3, 1+√36) and (-3, 1-√36).

21.

Graph the equation $9x^2 + 25y^2 = 225$ on the provided grid. Fill in the following: Center: __________, Vertices: __________, Co-Vertices: __________, Foci: __________.

a)

Center: (0,0), Vertices: (±5,0), Co-Vertices: (0,±3), Foci: (±√16,0).

b)

Center: (0,0), Vertices: (±3,0), Co-Vertices: (0,±5), Foci: (±√7,0).

c)

Center: (0,0), Vertices: (±5,0), Co-Vertices: (0,±3), Foci: (±√7,0).

d)

Center: (0,0), Vertices: (±3,0), Co-Vertices: (0,±5), Foci: (±√16,0).

22.

Graph the equation $27(x-1)^2 + 36(y+2)^2 = 972$ on the provided grid. Fill in the following: Center: __________, Vertices: __________, Co-Vertices: __________, Foci: __________.

a)

Center: (1, -2), Vertices: (1, 4) and (1, -8), Co-Vertices: (4, -2) and (-2, -2), Foci: (1, 5) and (1, -9).

b)

Center: (1, -2), Vertices: (1, 4) and (1, -8), Co-Vertices: (4, -2) and (-2, -2), Foci: (1, 6) and (1, -10).

c)

Center: (1, -2), Vertices: (1, 5) and (1, -9), Co-Vertices: (4, -2) and (-2, -2), Foci: (1, 6) and (1, -10).

d)

Center: (1, -2), Vertices: (1, 4) and (1, -8), Co-Vertices: (5, -2) and (-3, -2), Foci: (1, 5) and (1, -9).

23.

Graph the equation $9x^2 + y^2 + 144x = -567$ on the provided grid. Fill in the following: Center: __________, Vertices: __________, Co-Vertices: __________, Foci: __________.

a)

Center: (-8, 0), Vertices: (-8, 9) and (-8, -9), Co-Vertices: (-17, 0) and (1, 0), Foci: (-8, 10) and (-8, -10).

b)

Center: (8, 0), Vertices: (8, 9) and (8, -9), Co-Vertices: (17, 0) and (-1, 0), Foci: (8, 10) and (8, -10).

c)

Center: (0, -8), Vertices: (9, -8) and (-9, -8), Co-Vertices: (0, -17) and (0, 1), Foci: (10, -8) and (-10, -8).

d)

Center: (0, 8), Vertices: (9, 8) and (-9, 8), Co-Vertices: (0, 17) and (0, -1), Foci: (10, 8) and (-10, 8).

24.

Directions: Label a, b, c, h, and k on each diagram. Then give the standard form for the equation of an ellipse. HORIZONTAL ELLIPSE: Standard Form: __________

a)

(x-h)²/a² + (y-k)²/b² = 1

b)

(x-k)²/a² + (y-h)²/b² = 1

c)

(x-h)²/b² + (y-k)²/a² = 1

d)

(x-k)²/b² + (y-h)²/a² = 1

25.

Directions: Label a, b, c, h, and k on each diagram. Then give the standard form for the equation of an ellipse. VERTICAL ELLIPSE: Standard Form: __________

a)

(x-h)²/a² + (y-k)²/b² = 1

b)

(x-h)²/b² + (y-k)²/a² = 1

c)

(x-k)²/a² + (y-h)²/b² = 1

d)

(x-k)²/b² + (y-h)²/a² = 1

26.

Directions: Identify the correct equation for the ellipse with the given properties. Center: (0,0), Vertices: (±5,0), Co-Vertices: (0,±3), Foci: (±4,0).

a)

x²/25 + y²/9 = 1

b)

x²/9 + y²/25 = 1

c)

x²/16 + y²/9 = 1

d)

x²/25 + y²/16 = 1

27.

Directions: Write an equation for each ellipse. Identify the center, vertices, co-vertices, and foci. 2. Equation: __________ Center: __________ Vertices: __________ Co-Vertices: __________ Foci: __________

a)

Equation: $(x^2/4)$ + $(y^2/9)$ = 1; Center: (0,0); Vertices: (0,3), (0,-3); Co-Vertices: (2,0), (-2,0); Foci: (0, $\sqrt{5}$ ), (0,- $\sqrt{5}$ )

b)

Equation: $(x^2/9)$ + $(y^2/4)$ = 1; Center: (0,0); Vertices: $(3,0)$ , $(-3,0)$ ; Co-Vertices: $(0,2)$ , $(0,-2)$ ; Foci: $(\sqrt{5},0)$ , $(-\sqrt{5},0)$

c)

Equation: $(x^2/16)$ + $(y^2/25)$ = 1; Center: (0,0); Vertices: (0,5), (0,-5); Co-Vertices: (4,0), (-4,0); Foci: (0, $\sqrt{21}$ ), (0,- $\sqrt{21}$ )

d)

Equation: $(x^2/25)$ + $(y^2/16)$ = 1; Center: (0,0); Vertices: $(5,0)$ , $(-5,0)$ ; Co-Vertices: $(0,4)$ , $(0,-4)$ ; Foci: $(\sqrt{21},0)$ , $(-\sqrt{21},0)$

28.

Directions: Write an equation for each ellipse. Identify the center, vertices, co-vertices, and foci. 3. What is the equation of the ellipse with center (0,0), vertices at (±5,0), and co-vertices at (0,±3)?

a)

x²/25 + y²/9 = 1

b)

x²/9 + y²/25 = 1

c)

x²/16 + y²/9 = 1

d)

x²/9 + y²/16 = 1

29.

Directions: Write an equation for each ellipse with the given information. Vertices: (0, -9) and (0, 9) Co-Vertices: (-8, 0) and (8, 0)

a)

$(x^2/64) + (y^2/81) = 1$

b)

$(x^2/81) + (y^2/64) = 1$

c)

$(x^2/64) - (y^2/81) = 1$

d)

$(x^2/81) - (y^2/64) = 1$

30.

Directions: Write an equation for each ellipse with the given information. Vertices: (-3, 0) and (3, 0) Co-Vertices: (0, -1) and (0, 1)

a)

$x^2/9 + y^2 = 1$

b)

$x^2/9 + y^2/1 = 1$

c)

$x^2/3 + y^2/1 = 1$

d)

$x^2/3 + y^2 = 1$

31.

Directions: Write an equation for each ellipse with the given information. Vertices: (12, -4) and (-10, -4) Co-Vertices: (1, 2) and (1, -10)

a)

$(x-1)^2/121 + (y+4)^2/49 = 1$

b)

$(x+1)^2/121 + (y-4)^2/49 = 1$

c)

$(x+1)^2/49 + (y+4)^2/121 = 1$

d)

$(x-1)^2/49 + (y-4)^2/121 = 1$

32.

Directions: Write an equation for each ellipse with the given information. Vertices: (-2, 17) and (-2, 3) Co-Vertices: (2, 10) and (-6, 10)

a)

$(x + 2)^2/16 + (y - 10)^2/49 = 1$

b)

$(x - 2)^2/49 + (y + 10)^2/16 = 1$

c)

$(x + 2)^2/49 + (y - 10)^2/16 = 1$

d)

$(x - 2)^2/16 + (y + 10)^2/49 = 1$

33.

Directions: Write an equation for each ellipse with the given information. Vertices: (12, 2) and (2, 2) Foci: (10, 2) and (4, 2)

a)

$(x-7)^2/25 + (y-2)^2/9 = 1$

b)

$(x-7)^2/9 + (y-2)^2/25 = 1$

c)

$(x-7)^2/16 + (y-2)^2/9 = 1$

d)

$(x-7)^2/9 + (y-2)^2/16 = 1$

34.

Directions: Write an equation for each ellipse with the given information. Vertices: (-4, -7) and (-4, 7) Foci: (-4, -√13) and (-4, √13)

a)

$(x + 4)^2/49 + y^2/13 = 1$

b)

$(x + 4)^2/13 + y^2/49 = 1$

c)

$(x - 4)^2/49 + y^2/13 = 1$

d)

$(x - 4)^2/13 + y^2/49 = 1$

35.

Directions: Write an equation for each ellipse with the given information. Co-Vertices: (16, -3) and (-8, -3) Foci: (4, 2) and (4, -8)

a)

$(x - 4)^2/64 + (y + 3)^2/25 = 1$

b)

$(x - 4)^2/25 + (y + 3)^2/64 = 1$

c)

$(x + 4)^2/64 + (y - 3)^2/25 = 1$

d)

$(x + 4)^2/25 + (y - 3)^2/64 = 1$

36.

Directions: Write an equation for each ellipse with the given information. Co-Vertices: (1, -13) and (1, 3) Foci: (-5, -5) and (7, -5)

a)

$(x-1)^2/36 + (y+5)^2/64 = 1$

b)

$(x+1)^2/36 + (y-5)^2/64 = 1$

c)

$(x-1)^2/64 + (y+5)^2/36 = 1$

d)

$(x+1)^2/64 + (y-5)^2/36 = 1$

37.

Directions: Graph each hyperbola. Identify the center, vertices, co-vertices, foci, and asymptotes. 1. $\frac{x^2}{64} - \frac{y^2}{16} = 1$ Center: __________ Vertices: __________ Co-Vertices: __________ Foci: __________ Asymptotes: __________

a)

1. $\frac{x^2}{64} - \frac{y^2}{16} = 1$

b)

2. $\frac{y^2}{64} - \frac{x^2}{16} = 1$

c)

3. $\frac{x^2}{16} - \frac{y^2}{64} = 1$

d)

4. $\frac{y^2}{16} - \frac{x^2}{64} = 1$

38.

Directions: Graph each hyperbola. Identify the center, vertices, co-vertices, foci, and asymptotes. 2. $\frac{y^2}{25} - \frac{x^2}{1} = 1$ Center: __________ Vertices: __________ Co-Vertices: __________ Foci: __________ Asymptotes: __________

a)

Center: (0, 0) Vertices: (0, 5), (0, -5) Co-Vertices: (1, 0), (-1, 0) Foci: (0, √26), (0, -√26) Asymptotes: y = ±5x

b)

Center: (1, 1) Vertices: (1, 6), (1, -4) Co-Vertices: (2, 1), (0, 1) Foci: (1, √30), (1, -√20) Asymptotes: y = ±4x

c)

Center: (0, 0) Vertices: (0, 4), (0, -4) Co-Vertices: (1, 0), (-1, 0) Foci: (0, √20), (0, -√20) Asymptotes: y = ±4x

d)

Center: (0, 0) Vertices: (0, 5), (0, -5) Co-Vertices: (2, 0), (-2, 0) Foci: (0, √29), (0, -√29) Asymptotes: y = ±5x

39.

Directions: Graph each hyperbola. Identify the center, vertices, co-vertices, foci, and asymptotes. 3. $\frac{(x+6)^2}{4} - \frac{(y-1)^2}{4} = 1$ Center: __________ Vertices: __________ Co-Vertices: __________ Foci: __________ Asymptotes: __________

a)

Center: (-6, 1) Vertices: (-4, 1) and (-8, 1) Co-Vertices: (-6, 3) and (-6, -1) Foci: (-3, 1) and (-9, 1) Asymptotes: y = 1 ± (x + 6)

b)

Center: (6, -1) Vertices: (4, -1) and (8, -1) Co-Vertices: (6, 3) and (6, -3) Foci: (3, -1) and (9, -1) Asymptotes: y = -1 ± (x - 6)

c)

Center: (-6, 1) Vertices: (-6, 5) and (-6, -3) Co-Vertices: (-2, 1) and (-10, 1) Foci: (-6, 6) and (-6, -4) Asymptotes: y = 1 ± 2(x + 6)

d)

Center: (-6, 1) Vertices: (-4, 1) and (-8, 1) Co-Vertices: (-6, 3) and (-6, -1) Foci: (-3, 1) and (-9, 1) Asymptotes: y = 1 ± 2(x + 6)

40.

Directions: Graph each hyperbola. Identify the center, vertices, co-vertices, foci, and asymptotes. 4. $\frac{(y-2)^2}{49} - \frac{(x+2)^2}{9} = 1$ Center: __________ Vertices: __________ Co-Vertices: __________ Foci: __________ Asymptotes: __________

a)

Center: (-2, 2) Vertices: (5, 2) and (-9, 2) Co-Vertices: (-2, 5) and (-2, -1) Foci: (8, 2) and (-12, 2) Asymptotes: y = 2 ± (7/3)(x + 2)

b)

Center: (2, -2) Vertices: (2, 9) and (2, -5) Co-Vertices: (5, -2) and (-1, -2) Foci: (2, 12) and (2, -8) Asymptotes: y = -2 ± (3/7)(x - 2)

c)

Center: (-2, 2) Vertices: (2, 9) and (2, -5) Co-Vertices: (5, 2) and (-1, 2) Foci: (2, 12) and (2, -8) Asymptotes: y = 2 ± (3/7)(x + 2)

d)

Center: (-2, 2) Vertices: (-2, 9) and (-2, -5) Co-Vertices: (1, 2) and (-5, 2) Foci: (-2, 12) and (-2, -8) Asymptotes: y = 2 ± (7/3)(x + 2)

41.

Given the equation $9y^2 - 3x^2 + 1 = x^2 + 37$ , fill in the following details: Center: __________, Vertices: __________, Co-Vertices: __________, Foci: __________, Asymptotes: __________.

a)

Center: (0,0), Vertices: (±3,0), Co-Vertices: (0,±1), Foci: (±√10,0), Asymptotes: y=±(1/3)x.

b)

Center: (0,0), Vertices: (±3,0), Co-Vertices: (0,±2), Foci: (±√13,0), Asymptotes: y=±(2/3)x.

c)

Center: (0,0), Vertices: (±2,0), Co-Vertices: (0,±3), Foci: (±√5,0), Asymptotes: y=±(3/2)x.

d)

Center: (0,0), Vertices: (±1,0), Co-Vertices: (0,±3), Foci: (±√7,0), Asymptotes: y=±(3)x.

42.

Given the equation $4x^2 - y^2 - 6y = 25$ , fill in the following details: Center: __________, Vertices: __________, Co-Vertices: __________, Foci: __________, Asymptotes: __________.

a)

Center: (0, 3), Vertices: (0, 8) and (0, -2), Co-Vertices: (2, 3) and (-2, 3), Foci: (0, 9) and (0, -3), Asymptotes: y = 3 ± (1/2)x

b)

Center: (0, 0), Vertices: (0, 5) and (0, -5), Co-Vertices: (3, 0) and (-3, 0), Foci: (0, 6) and (0, -6), Asymptotes: y = ±(3/4)x

c)

Center: (1, 1), Vertices: (1, 6) and (1, -4), Co-Vertices: (4, 1) and (-2, 1), Foci: (1, 7) and (1, -5), Asymptotes: y = 1 ± (2/3)x

d)

Center: (2, 2), Vertices: (2, 7) and (2, -3), Co-Vertices: (5, 2) and (-1, 2), Foci: (2, 8) and (2, -4), Asymptotes: y = 2 ± (3/5)x

43.

Given the equation $x^2 - 16y^2 - 2x = 63$ , fill in the following details: Center: __________, Vertices: __________, Co-Vertices: __________, Foci: __________, Asymptotes: __________.

a)

Center: (1, 0), Vertices: (5, 0) and (-3, 0), Co-Vertices: (1, 4) and (1, -4), Foci: (6, 0) and (-4, 0), Asymptotes: y = ±(1/4)(x - 1).

b)

Center: (0, 0), Vertices: (4, 0) and (-4, 0), Co-Vertices: (0, 4) and (0, -4), Foci: (5, 0) and (-5, 0), Asymptotes: y = ±(1/4)x.

c)

Center: (1, 0), Vertices: (4, 0) and (-4, 0), Co-Vertices: (1, 3) and (1, -3), Foci: (5, 0) and (-5, 0), Asymptotes: y = ±(1/3)(x - 1).

d)

Center: (0, 0), Vertices: (5, 0) and (-5, 0), Co-Vertices: (0, 3) and (0, -3), Foci: (6, 0) and (-6, 0), Asymptotes: y = ±(1/3)x.

44.

Given the equation $-x^2 + 9y^2 - 4x + 72y = -131$ , fill in the following details: Center: __________, Vertices: __________, Co-Vertices: __________, Foci: __________, Asymptotes: __________.

a)

Center: (2, -4), Vertices: (2, -13) and (2, 5), Co-Vertices: (5, -4) and (-1, -4), Foci: (2, -15) and (2, 7), Asymptotes: y = ±3/2(x - 2)

b)

Center: (0, 0), Vertices: (0, -9) and (0, 9), Co-Vertices: (3, 0) and (-3, 0), Foci: (0, -10) and (0, 10), Asymptotes: y = ±3/2x

c)

Center: (1, -3), Vertices: (1, -12) and (1, 6), Co-Vertices: (4, -3) and (-2, -3), Foci: (1, -14) and (1, 8), Asymptotes: y = ±3/2(x - 1)

d)

Center: (3, -5), Vertices: (3, -14) and (3, 4), Co-Vertices: (6, -5) and (0, -5), Foci: (3, -16) and (3, 6), Asymptotes: y = ±3/2(x - 3)

45.

Label a, b, c, h, and k on each diagram. Then give the standard form for the equation of a horizontal hyperbola.

a)

Standard Form:

b)

Standard Form: $(x-h)^2/a^2 - (y-k)^2/b^2 = 1$

c)

Standard Form: $(y-k)^2/a^2 - (x-h)^2/b^2 = 1$

d)

Standard Form: $(x-k)^2/a^2 - (y-h)^2/b^2 = 1$

46.

Directions: Label a, b, c, h, and k on each diagram. Then give the standard form for the equation of a vertical hyperbola. Standard Form:

a)

What is the standard form for the equation of a vertical hyperbola?

b)

What is the standard form for the equation of a horizontal hyperbola?

c)

What is the standard form for the equation of a circle?

d)

What is the standard form for the equation of an ellipse?

47.

Directions: Write an equation for each hyperbola. 1. (Diagram provided)

a)

$x^2/a^2 - y^2/b^2 = 1$

b)

$y^2/a^2 - x^2/b^2 = 1$

c)

$x^2/b^2 - y^2/a^2 = 1$

d)

$y^2/b^2 - x^2/a^2 = 1$

48.

Directions: Write an equation for each hyperbola. 2. (Diagram provided)

a)

$x^2/a^2 - y^2/b^2 = 1$

b)

$y^2/a^2 - x^2/b^2 = 1$

c)

$x^2/b^2 - y^2/a^2 = 1$

d)

$y^2/b^2 - x^2/a^2 = 1$

49.

Directions: Write an equation for each hyperbola with the given information. 3. Vertices: (0, ±3) Co-Vertices: (±1, 0)

a)

$x^2/1^2 - y^2/3^2 = 1$

b)

$y^2/3^2 - x^2/1^2 = 1$

c)

$x^2/3^2 - y^2/1^2 = 1$

d)

$y^2/1^2 - x^2/3^2 = 1$

50.

Directions: Write an equation for each hyperbola with the given information. 4. Vertices: (14, -4) and (-4, -4) Co-Vertices: (5, 1) and (5, -9)

a)

$(x-5)^2/81 - (y+4)^2/25 = 1$

b)

$(x+5)^2/81 - (y-4)^2/25 = 1$

c)

$(x-5)^2/25 - (y+4)^2/81 = 1$

d)

$(x+5)^2/25 - (y-4)^2/81 = 1$

51.

Directions: Write an equation for each hyperbola with the given information. 5. Vertices: (4, -6) and (-6, -6) Co-Vertices: (-1, 3) and (-1, -15)

a)

$(x+1)^2/25 - (y+6)^2/81 = 1$

b)

$(x-1)^2/25 - (y+6)^2/81 = 1$

c)

$(x+1)^2/81 - (y+6)^2/25 = 1$

d)

$(x-1)^2/81 - (y+6)^2/25 = 1$

52.

Directions: Write an equation for each hyperbola with the given information. 6. Vertices: (-2, -8) and (-2, 8) Co-Vertices: (-6, 0) and (2, 0)

a)

$(y + 0)^2/8^2 - (x + 2)^2/4^2 = 1$

b)

$(x + 2)^2/8^2 - (y + 0)^2/4^2 = 1$

c)

$(y + 8)^2/8^2 - (x + 0)^2/4^2 = 1$

d)

$(x + 0)^2/8^2 - (y + 2)^2/4^2 = 1$

53.

Write the equation of the hyperbola with the given vertices and foci. Vertices: (±1, 0), Foci: (±√37, 0).

a)

$x^2/1 - y^2/36 = 1$

b)

$x^2/1 - y^2/37 = 1$

c)

$x^2/36 - y^2/1 = 1$

d)

$x^2/37 - y^2/1 = 1$

54.

Write the equation of the hyperbola with the given vertices and foci. Vertices: (-4, -9) and (-10, -9), Foci: (-2, -9) and (-12, -9).

a)

$(x + 7)^2/9 - (y + 9)^2/25 = 1$

b)

$(x + 7)^2/25 - (y + 9)^2/9 = 1$

c)

$(x + 7)^2/16 - (y + 9)^2/9 = 1$

d)

$(x + 7)^2/9 - (y + 9)^2/16 = 1$

55.

Write the equation of the hyperbola with the given vertices and foci. Vertices: (4, 11) and (4, -13), Foci: (4, 12) and (4, -14).

a)

$(y - 1)^2/144 - (x - 4)^2/1 = 1$

b)

$(y - 2)^2/169 - (x - 4)^2/1 = 1$

c)

$(y - 3)^2/169 - (x - 4)^2/1 = 1$

d)

$(y - 4)^2/144 - (x - 4)^2/1 = 1$

56.

Write the equation of the hyperbola with the given vertices and foci. Vertices: (0, 9) and (0, 5), Foci: (0, 7 ± √29).

a)

$(y - 7)^2/4 - x^2/29 = 1$

b)

$(y - 7)^2/16 - x^2/29 = 1$

c)

$(y - 7)^2/4 - x^2/16 = 1$

d)

$(y - 7)^2/29 - x^2/4 = 1$

57.

Write the equation of the hyperbola with the given co-vertices and foci. Co-Vertices: (-2, 3) and (-8, 3), Foci: (-5, 8) and (-5, -2).

a)

$(x + 5)^2/9 - (y - 3)^2/25 = 1$

b)

$(y - 3)^2/9 - (x + 5)^2/25 = 1$

c)

$(x + 5)^2/25 - (y - 3)^2/9 = 1$

d)

$(y - 3)^2/25 - (x + 5)^2/9 = 1$

58.

Write the equation of the hyperbola with the given co-vertices and foci. Co-Vertices: (8, -1) and (8, -5), Foci: (8 ± √5, -3).

a)

$(y + 3)^2/4 - (x - 8)^2/5 = 1$

b)

$(x - 8)^2/4 - (y + 3)^2/5 = 1$

c)

$(y + 3)^2/5 - (x - 8)^2/4 = 1$

d)

$(x - 8)^2/5 - (y + 3)^2/4 = 1$

59.

Challenge! Write the equation of the hyperbola with the given vertices and asymptotes. Vertices: (±6, 0), Asymptotes: y = ±1/3 x.

a)

$x^2/36 - y^2/12 = 1$

b)

$x^2/36 + y^2/12 = 1$

c)

$x^2/12 - y^2/36 = 1$

d)

$x^2/12 + y^2/36 = 1$

60.

Challenge! Write the equation of the hyperbola with the given co-vertices and asymptotes. Co-Vertices: (1, -1) and (5, -1), Asymptotes: y = 2x - 7 and y = -2x + 5.

a)

$(x - 3)^2/4 - (y + 1)^2/16 = 1$

b)

$(x - 3)^2/16 - (y + 1)^2/4 = 1$

c)

$(x - 3)^2/4 + (y + 1)^2/16 = 1$

d)

$(x - 3)^2/16 + (y + 1)^2/4 = 1$

61.

Directions: Identify the vertex, axis of symmetry, focus, and directrix of the parabola $y^2 = 4x$ . What is the vertex of the parabola?

a)

(0, 0)

b)

(1, 0)

c)

(0, 1)

d)

(1, 1)

62.

Directions: Graph each parabola. Identify the vertex, axis of symmetry, focus, and directrix for the equation $x^2 = -12y$ . What is the vertex?

a)

(0, 0)

b)

(0, -3)

c)

(3, 0)

d)

(-3, 0)

63.

Directions: Graph each parabola. Identify the vertex, axis of symmetry, focus, and directrix. 3. $(x-2)^2 = 6(y+4)$ What is the vertex of the parabola?

a)

(2, -4)

b)

(-2, 4)

c)

(2, 4)

d)

(-2, -4)

64.

Directions: Graph each parabola. Identify the vertex, axis of symmetry, focus, and directrix. 4. $(y-5)^2 = -16(x-1)$ What is the vertex of the parabola?

a)

(1, 5)

b)

(5, 1)

c)

(-1, 5)

d)

(1, -5)

65.

Given the equation $\frac{1}{20}x^2 + 6 = y$ , fill in the following: Vertex: __________, Axis of Sym: __________, Focus: __________, Directrix: __________.

a)

Vertex: (0, 6), Axis of Sym: x = 0, Focus: (0, 6.025), Directrix: y = 5.975.

b)

Vertex: (0, 0), Axis of Sym: x = 0, Focus: (0, 0.025), Directrix: y = -0.025.

c)

Vertex: (0, 6), Axis of Sym: y = 0, Focus: (0, 6.025), Directrix: x = 5.975.

d)

Vertex: (0, 6), Axis of Sym: x = 0, Focus: (0, 5.975), Directrix: y = 6.025.

66.

Given the equation $-\frac{1}{8}(y + 3)^2 = x - 3$ , fill in the following: Vertex: __________, Axis of Sym: __________, Focus: __________, Directrix: __________.

a)

Vertex: (3, -3), Axis of Sym: y = -3, Focus: (2.875, -3), Directrix: x = 3.125

b)

Vertex: (3, 3), Axis of Sym: y = 3, Focus: (3.125, 3), Directrix: x = 2.875

c)

Vertex: (-3, 3), Axis of Sym: y = 3, Focus: (-3.125, 3), Directrix: x = -2.875

d)

Vertex: (-3, -3), Axis of Sym: y = -3, Focus: (-2.875, -3), Directrix: x = -3.125

67.

Given the equation $y^2 + 4x + 10y + 33 = 0$ , fill in the following: Vertex: __________, Axis of Sym: __________, Focus: __________, Directrix: __________.

a)

Vertex: (-2, -5), Axis of Sym: y = -5, Focus: (-1, -5), Directrix: x = -3.

b)

Vertex: (-2, -5), Axis of Sym: x = -2, Focus: (-2, -4), Directrix: x = -3.

c)

Vertex: (-2, -5), Axis of Sym: y = -5, Focus: (-2, -6), Directrix: x = -3.

d)

Vertex: (-2, -5), Axis of Sym: y = -5, Focus: (-2, -5), Directrix: x = -3.

68.

Given the equation $x^2 - 6x - 18y - 27 = 0$ , fill in the following: Vertex: __________, Axis of Sym: __________, Focus: __________, Directrix: __________.

a)

Vertex: (3, 0), Axis of Sym: x = 3, Focus: (3, 1/4), Directrix: y = -1/4.

b)

Vertex: (3, 0), Axis of Sym: y = 3, Focus: (3, 1/4), Directrix: x = -1/4.

c)

Vertex: (0, 3), Axis of Sym: x = 3, Focus: (1/4, 3), Directrix: y = -1/4.

d)

Vertex: (3, 0), Axis of Sym: x = 3, Focus: (3, -1/4), Directrix: y = 1/4.

69.

Directions: Label p, h, and k on each diagram and give the equation of the parabola in standard form. Write an equation for each parabola. Diagram 1.

a)

Label p, h, and k on each diagram and give the equation of the parabola in standard form.

b)

Label p, h, and k on each diagram and give the equation of the parabola in vertex form.

c)

Label p, h, and k on each diagram and give the equation of the parabola in factored form.

d)

Label p, h, and k on each diagram and give the equation of the parabola in general form.

70.

Directions: Label p, h, and k on each diagram and give the equation of the parabola in standard form. Write an equation for each parabola. Diagram 2.

a)

Label p, h, and k on the diagram and write the equation of the parabola.

b)

Label p, h, and k on the diagram and provide the vertex form of the parabola.

c)

Identify the vertex and focus of the parabola and write its equation.

d)

Label the axis of symmetry and write the equation of the parabola.

71.

Directions: Label p, h, and k on each diagram and give the equation of the parabola in standard form. Write an equation for each parabola. Diagram 3.

a)

Label p, h, and k on the diagram and write the equation of the parabola.

b)

Label p, h, and k on the diagram only.

c)

Write the equation of the parabola only.

d)

None of the above.

72.

Directions: Label p, h, and k on each diagram and give the equation of the parabola in standard form. Write an equation for each parabola. Diagram 4.

a)

Label p, h, and k on each diagram and give the equation of the parabola in standard form.

b)

Label p, h, and k on each diagram and give the equation of the parabola in vertex form.

c)

Label p, h, and k on each diagram and give the equation of the parabola in factored form.

d)

Label p, h, and k on each diagram and give the equation of the parabola in general form.

73.

Directions: Write an equation for each parabola with the given information. Vertex: (0, 0); Focus: (2, 0).

a)

$y^2 = 8x$

b)

$x^2 = 8y$

c)

$y^2 = 4x$

d)

$x^2 = 4y$

74.

Directions: Write an equation for each parabola with the given information. Vertex: (0, 0); Focus: $\left(0, -\frac{7}{4}\right)$ .

a)

y = $\frac{1}{7}x^2$

b)

y = $-\frac{1}{7}x^2$

c)

y = $\frac{4}{7}x^2$

d)

y = $-\frac{4}{7}x^2$

75.

Given the vertex (-6, -5) and focus (-6, -4), find the equation of the parabola.

a)

y = $(x + 6)^2 - 5$

b)

$y = (x + 6)^2 + 5$

c)

$x = (y + 5)^2 - 6$

d)

$x = (y + 5)^2 + 6$

76.

Given the vertex (3, -4) and focus $\left( \frac{1}{2}, -4 \right)$ , find the equation of the parabola.

a)

y + 4 = $-\frac{1}{5}(x - 3)^2$

b)

y + 4 = $\frac{1}{5}(x - 3)^2$

c)

y - 4 = $-\frac{1}{5}(x + 3)^{2}$

d)

y - 4 = $\frac{1}{5}(x + 3)^2$

77.

Given the vertex (0, 0) and directrix y = -5, find the equation of the parabola.

a)

y = $(\frac{1}{20})x^2$

b)

y = $(\frac{1}{10})x^2$

c)

y = $(\frac{1}{5})x^2$

d)

$y = 5x^2$

78.

Given the vertex (-4, -2) and directrix x = -7, find the equation of the parabola.

a)

$(y + 2)^2 = 12(x + 4)$

b)

$(y - 2)^2 = -12(x + 4)$

c)

$(x + 4)^2 = 12(y + 2)$

d)

$(x + 4)^2 = -12(y + 2)$

79.

Given the vertex (5, 0) and directrix y = 6, find the equation of the parabola.

a)

y = $(x - 5)^2 - 6$

b)

$(x - 5)^2 + 6$

c)

y = $-\frac{1}{4} (x - 5)^2$

d)

y = $\frac{1}{4} (x - 5)^2$

80.

Given the vertex (-1, -1) and directrix x = $-\frac{1}{2}$ , find the equation of the parabola.

a)

$y = (x + 1)^2 - 1$

b)

$x = (y + 1)^2 - 1$

c)

$y = (x - 1)^2 + 1$

d)

$x = (y - 1)^2 + 1$

81.

Given the focus (0, -6) and directrix y = 6, find the equation of the parabola.

a)

y = $(1/24)x^2 - 6$

b)

y = $(1/24)x^2 + 6$

c)

y = $(\frac{1}{12})x^2 - 6$

d)

y = $(1/12)x^2 + 6$

82.

Given the focus (-1, 5) and directrix x = 7, find the equation of the parabola.

a)

$(x + 1)^2 = 20(y - 5)$

b)

$(y - 5)^2 = 20(x + 1)$

c)

$(x - 1)^2 = 20(y + 5)$

d)

$(y + 5)^2 = 20(x - 1)$

83.

Given the focus (6, -4) and directrix x = 0, find the equation of the parabola.

a)

$x^2 = 24y$

b)

$y^2 = 24x$

c)

$(x - 6)^2 = -24(y + 4)$

d)

$(y + 4)^2$ = 24 $(x - 6)$

84.

Given the focus $\left( -7, \frac{17}{4} \right)$ and directrix y = -\frac{1}{4}, find the equation of the parabola.

a)

y = $\frac{1}{8}(x + 7)^2 + \frac{17}{4}$

b)

y = $\frac{1}{8}(x + 7)^2 - \frac{17}{4}$

c)

y = $\frac{1}{4}(x + 7)^2 + \frac{17}{4}$

d)

y = $\frac{1}{4}(x + 7)^2 - \frac{17}{4}$

85.

Directions: State the conic represented by each equation below. 1. $9x^2 - 4y^2 - 36x + 16y - 16 = 0$

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

86.

Directions: State the conic represented by each equation below. 2. $x^2 + y^2 + 4x - 8y + 11 = 0$

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

87.

Directions: State the conic represented by each equation below. 3. $y^2 - x - 10y + 28 = 0$

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

88.

Directions: State the conic represented by each equation below. What type of conic is represented by the equation $49x^2 + 4y^2 - 98x - 147 = 0$ ?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

89.

Determine the type of conic for the equation $x^2 + y^2 - 14x - 6y + 57 = 0$ .

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

90.

Directions: Determine the type of conic, write the equation in standard form, then graph. 6. $16x^2 + 25y^2 + 64x - 50y - 311 = 0$

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

91.

Directions: Determine the type of conic from the equation $y^2 + x + 2y = 0$ .

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

92.

Directions: Determine the type of conic from the equation $-x^2 + y^2 + 6x + 6y - 4 = 0$ .

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

93.

Which of the following is the correct graph of the equation $2x^2 - 8x - 3y + 11 = 0$ ?

a)

Graph A

b)

Graph B

c)

Graph C

d)

Graph D

94.

Which of the following represents the graph of the equation $x^2 + y^2 - 8x - 20 = 0$ ?

a)

A circle centered at (4, 0) with radius 4

b)

A circle centered at (4, 0) with radius 2

c)

A circle centered at (0, 4) with radius 4

d)

A circle centered at (0, 4) with radius 2

95.

Graph the equation $4x^2 + y^2 - 56x + 6y + 189 = 0$ on the provided grid.

a)

The graph is a circle centered at (7, -3) with radius 5.

b)

The graph is an ellipse centered at (7, -3) with semi-major axis 5.

c)

The graph is a parabola opening upwards.

d)

The graph is a hyperbola centered at (7, -3).

96.

Graph the equation $x^2 - y^2 - 25 = 0$ on the provided grid.

a)

The graph is a hyperbola centered at the origin.

b)

The graph is a circle centered at the origin.

c)

The graph is a parabola opening upwards.

d)

The graph is a line.

97.

Which of the following represents the graph of the equation $2x^2 + 2y^2 + 12x - 20y + 60 = 0$ ?

a)

A circle centered at (-3, 5) with radius 4

b)

An ellipse centered at (-3, 5) with semi-major axis 4

c)

A parabola opening upwards

d)

A hyperbola centered at (-3, 5)

98.

Graph the equation $y^2 - 12x - 2y - 71 = 0$ on the provided grid.

a)

The graph is a parabola opening to the right.

b)

The graph is a parabola opening to the left.

c)

The graph is a circle.

d)

The graph is an ellipse.

99.

Directions: Solve each system of equations by graphing. Identify all possible solutions. 1. $y = x^2 + 6x$ $y = x - 4$ What are the solutions?

a)

(-2, -6) and (2, -2)

b)

(-3, -7) and (3, -1)

c)

(-4, -8) and (4, 0)

d)

(-5, -9) and (5, 1)

100.

Directions: Solve each system of equations by graphing. Identify all possible solutions. 2. $y = x^2 + 6x + 2$ $y = -x - 8$ What are the solutions?

a)

(-5, -3) and (-1, -7)

b)

(0, -8) and (2, -10)

c)

(-4, -4) and (1, -9)

d)

(-6, -2) and (0, -8)

Unit 9: Conic Sections - review

Total questions: 100

Worksheet time: 50mins

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