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: __________.

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).

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).

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).

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).

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

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

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

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

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

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: __________.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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: __________

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

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

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

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

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: __________

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

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

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

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

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: __________

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)

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)

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)

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)

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: __________

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)

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)

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)

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)

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

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

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

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

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

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

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

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

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

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

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

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).

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.

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).

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.

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

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)

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

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)

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)

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

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

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

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

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:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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.

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

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

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

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

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.

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

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

Write the equation of the parabola only.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Unit 9: Conic Sections - review

Authored by Gordon Minton

Mathematics

9th Grade

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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Unit 9: Conic Sections - review

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

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

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

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

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

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

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

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

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