Quiz about Unit 9: Conic Sections - review

Question 1

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 2

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 3

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 5

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 6

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 7

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 8

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

Accepted Answer

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

Answer

Center: (1, 4), Radius: 81

Answer

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

Answer

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

Question 9

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 10

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

Accepted Answer

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

Answer

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

Answer

Center: (6, 0), Radius: 12

Answer

Center: (0, 6), Radius: 6

Question 11

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: _______

Accepted Answer

Center: (0, 0), Radius: 7

Answer

Center: (0, 0), Radius: 3

Answer

Center: (0, 0), Radius: 5

Answer

Center: (0, 0), Radius: 10

Question 12

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: _______

Accepted Answer

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

Answer

Center: (0, 7), Radius: 9

Answer

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

Answer

Center: (0, 7), Radius: 5

Question 13

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: _______

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 14

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?

Accepted Answer

(0, 0)

Answer

(8, 0)

Answer

(0, 3)

Answer

(8, 3)

Question 15

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?

Accepted Answer

(0, 0)

Answer

(1, 0)

Answer

(0, 1)

Answer

(1, 1)

Question 16

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?

Accepted Answer

(0, 0)

Answer

(1, 1)

Answer

(4, 0)

Answer

(0, 4)

Question 17

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?

Accepted Answer

(-1, -1)

Answer

(1, 1)

Answer

(0, 0)

Answer

(1, -1)

Question 18

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: __________.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 19

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 20

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

Accepted Answer

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,- $$\sqrt{5}$$ )

Answer

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

Answer

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,- $$\sqrt{21}$$ )

Answer

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

Question 21

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 22

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 24

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 25

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 26

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 27

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 28

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: __________

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 29

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

Accepted Answer

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

Answer

Standard Form:

Answer

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

Answer

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

Question 30

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:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 31

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 32

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 33

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)

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 34

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)

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 35

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)

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 36

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 37

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 38

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).

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 39

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.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 40

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

Accepted Answer

(0, 0)

Answer

(1, 0)

Answer

(0, 1)

Answer

(1, 1)

Question 41

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

Accepted Answer

(0, 0)

Answer

(0, -3)

Answer

(3, 0)

Answer

(-3, 0)

Question 42

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?

Accepted Answer

(2, -4)

Answer

(-2, 4)

Answer

(2, 4)

Answer

(-2, -4)

Question 43

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?

Accepted Answer

(1, 5)

Answer

(5, 1)

Answer

(-1, 5)

Answer

(1, -5)

Question 44

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 45

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 46

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 47

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 48

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.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 49

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.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 50

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.

Accepted Answer

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

Answer

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

Answer

Write the equation of the parabola only.

Answer

None of the above.

Question 51

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.

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 52

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

Accepted Answer

$$y^2 = 8x$$

Answer

$$x^2 = 8y$$

Answer

$$y^2 = 4x$$

Answer

$$x^2 = 4y$$

Question 53

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 54

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 55

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 56

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

Accepted Answer

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

Answer

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

Answer

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

Answer

$$y = 5x^2$$

Question 57

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 58

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 59

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 60

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 61

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 62

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

Accepted Answer

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

Answer

$$x^2 = 24y$$

Answer

$$y^2 = 24x$$

Answer

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

Question 63

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 64

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

Accepted Answer

Hyperbola

Answer

Circle

Answer

Ellipse

Answer

Parabola

Unit 9: Conic Sections - review

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