Determine the standard form equation of a circle given the center and radius.

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

Graph the equation $$\frac{(x+3)^2}{45} + \frac{(y-1)^2}{81} = 1$$ . Fill in: 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).

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

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

Graph the equation $$27(x-1)^2 + 36(y+2)^2 = 972$$ . Fill in: 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).

Graph the equation $$9x^2 + y^2 + 144x = -567$$ . Fill in: 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).

Write an equation for each ellipse. Identify the center, vertices, co-vertices, and foci.

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

Write an equation for the ellipse with vertices (0, -9) and (0, 9) and co-vertices (-8, 0) and (8, 0).

$$\frac{x^2}{64} + \frac{y^2}{81} = 1$$ .

Write an equation for the ellipse with vertices (-3, 0) and (3, 0), and co-vertices (0, -1) and (0, 1).

$$\frac{x^2}{9} + \frac{y^2}{1} = 1$$

Write an equation for the ellipse with vertices (12, -4) and (-10, -4) and co-vertices (1, 2) and (1, -10).

$$\frac{{(x-1)^2}}{{121}} + \frac{{(y+4)^2}}{{49}} = 1$$

Write an equation for the ellipse with vertices (-2, 17) and (-2, 3) and co-vertices (2, 10) and (-6, 10).

$$\frac{{(x + 2)^2}}{{16}} + \frac{{(y - 10)^2}}{{49}} = 1$$

Write an equation for the ellipse with vertices (12, 2) and (2, 2) and foci (10, 2) and (4, 2).

$$\frac{{(x-7)^2}}{{25}} + \frac{{(y-2)^2}}{{9}} = 1$$

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

$$\frac{{(x - 4)^2}}{{25}} + \frac{{(y + 3)^2}}{{64}} = 1$$ .

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

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

Graph the hyperbola: $$\frac{x^2}{64} - \frac{y^2}{16} = 1$$ . Identify the center, vertices, co-vertices, foci, and asymptotes.

Center: (0, 0), Vertices: (±8, 0), Co-Vertices: (0, ±4), Foci: (±√80, 0), Asymptotes: y = ±0.5x

Graph the hyperbola: $$\frac{y^2}{25} - \frac{x^2}{1} = 1$$ . Identify the center, vertices, co-vertices, foci, and asymptotes.

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

Graph the hyperbola: $$\frac{(x+6)^2}{4} - \frac{(y-1)^2}{4} = 1$$ . Identify the center, vertices, co-vertices, foci, and 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)

Graph the hyperbola: $$\frac{(y-2)^2}{49} - \frac{(x+2)^2}{9} = 1$$ . Identify the center, vertices, co-vertices, foci, and 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)

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.

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

Equation: $$x^2 - 16y^2 - 2x = 63$$ . Fill in: 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).

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)

Standard form for the equation of a horizontal hyperbola.

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

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

(y - k)^2/a^2 - (x - h)^2/b^2 = 1

Write an equation for the hyperbola with Vertices: (0, ±3) and Co-Vertices: (±1, 0).

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

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

$$\frac{{(x-5)^2}}{{81}} - \frac{{(y+4)^2}}{{25}} = 1$$

Unit 9: Conic Sections - Flashcard review Flashcards

Student preview

50 questions

Show all answers

1.

FLASHCARD QUESTION

Front

Equation of circle with center (-9, 0) and radius 1.

Back

2.

FLASHCARD QUESTION

Front

Equation of circle with center (3, -3) and radius 2√6

Back

3.

FLASHCARD QUESTION

Front

Equation of circle with Center: (4, 7), Endpoint: (-1, -2)

Back

4.

FLASHCARD QUESTION

Front

Equation of circle with Center: (0, -8), Endpoint: (2, -5)

Back

5.

FLASHCARD QUESTION

Front

Write the equation of the circle with endpoints of diameter: (-6, 2) and (-8, 10).

Back

6.

FLASHCARD QUESTION

Front

Equation of circle with endpoints of diameter: (-13, -7) and (11, 11)

Back

7.

FLASHCARD QUESTION

Front

Equation of a circle with center (h, k) and radius r.

Back

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