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# Ellipses Help (page 3)

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## Ellipses Practice Problems

#### Practice

1. Identify the center, foci, vertices, and eccentricity for

2. Identify the center, foci, vertices, and eccentricity for

3. Identify the center and radius for the circle

For Problems 4-7, match the equation with the graph in Figures 12.17-12.20.

Fig. 12.17

Fig. 12.18

Fig. 12.19

Fig. 12.20

#### Solutions

1. h = 0, k = 10, a = 13, b = 5,

Center: (0, 10)

Foci: ( hc , k ) = (0−12, 10) = (−12, 10) and ( h + c , k ) = (0 + 12, 10) (12, 10)

Vertices: ( ha , k ) = (0 − 13, 10) = (−13, 10) and ( h + a , k ) (0 + 13, 10) = (13, 10)

Eccentricity:

2. h = −9, k = −2, a = 29, b = 20,

Center: (−9, −2)

Foci: ( h , kc ) = (−9, −2−21) = (−9, −23) and ( h , k + c ) = (−9, −2 + 21) = (−9, 19)

Vertices: ( h , ka ) = (−9, −2 − 29) = (−9, −31) and ( h , k + a ) = (−9, −2 + 29) = (−9, 27)

Eccentricity:

3. The center is (−6, 1), and the radius is 7.

4. Figure 12.19

5. Figure 12.20

6. Figure 12.18

7. Figure 12.17

Practice problems for this concept can be found at: Conic Sections Practice Test.

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