Write the Standard-Form Equation of an Ellipse with the Given Characteristics. Sketch

Name

Class

Date

Translating Conic Sections

10-6

Practice

Form K

Write the standard-form equation of an ellipse with the given characteristics. Sketch the ellipse.

1. vertices (3, 2) and (7, 2), focus (6, 2)

center: (5, 2) h = , k =

b2 = a2 - c2 = 4 - 1=

2. vertices (-4, 1) and (-4, 13), focus (-4, 5) 3. vertices (1, 3) and (17, 3), focus (3, 3)

Identify the center, vertices, and foci of each hyperbola.

Compare to

center (h, k): vertices (h ± a,k): foci (h ± c,k):

5. 6.

Identify each conic section as a parabola or a circle by writing the equation in standard form and sketching the graph. For a parabola, give the vertex. For a circle, give the center and the radius.

7. x2 + y2 - 2x - 4y - 11 = 0 8. x2 - 2y - 8x = -10

Prentice Hall Foundations Algebra 2 • Teaching Resources

Name

Class

Date

Translating Conic Sections

10-6

Practice (continued)

Form K

Identify each conic section as an ellipse or a hyperbola by writing the equation in standard form and sketching the graph. Give the center and the foci.

9. x2 + 4y2 - 6x + 8y = –9 10. y2 - 4x2 + 8y - 16x = 4

11. The path that a comet travels is 8 units closer to one focus of a path than the other focus. The foci are located at (0, 0) and (160, 0).

a. What conic section models this problem?

The difference between the distances from the comet’s path to the two foci
is a constant 8 units. This is a .

b. What equation represents the path of the comet?

Constant difference = 8 units = 2a, so a = .

2c = 160, so c = .

b2 = c2 -a2 = .

The center of the hyperbola is midway between the foci, at .

The graph of each equation is to be translated 3 units right and 5 units down. Write each new equation.

12. y = 2(x-1)2+12 13.

14. y2 - 2x2 - 18y + 77 = 0 15. x2 + y2 + 2x - 6y = 21

Prentice Hall Foundations Algebra 2 • Teaching Resources