Write an Equation of an Ellipse in Standard Form with Center at the Origin with the Given

Name

Class

Date

10-4

Ellipses

Practice

Form K

Write an equation of an ellipse in standard form with center at the origin with the given vertex and co-vertex listed. (Note that the vertex is listed first and the co-vertex is listed second.)

1. (3, 0), (0, 1)

Because one vertex is at (3, 0), the other vertex is at (-3, 0).

The major axis is horizontal.

Because one co-vertex is at (0, 1), the other co-vertex is at (0, -1).

The minor axis is vertical.

Write the standard form of a horizontal ellipse.
Substitute for a2 and b2.

2. (0, -7), (2, 0)

3. (-5, 0), (0, -4)

Find the foci for each equation of an ellipse. Then graph the ellipse. 4. 16x2 + 25y2 = 400

vertices: (-5, 0) and (5, 0)

co-vertices: (0, -4) and (0, 4) foci: (-3, 0) and (3, 0)

Write the equation in standard form.

Find the vertices, co-vertices, and foci from the equation.

Plot the points to graph the ellipse.

6. 4x2 + 16y2 = 16

Find the distance between the foci of an ellipse. The lengths of the major and minor axes are listed respectively.

7. 26, 24

8. 30, 18

9. 18, 12

Prentice Hall Foundations Algebra 2 • Teaching Resources

Name

Class

Date

10-4

Ellipses

Practice (continued)

Form K

Write an equation of an ellipse for the given foci and co-vertices.

10. foci (0, ±3), co-vertices (±1, 0)

The foci are on the y-axis, so the major axis is vertical.

Because c = 3 and b = 1, c2 = 9 and b2 = 1.

c2 = a2 - b2

Find a2: 9 = a2 - 1 Write the equation:

11. foci (±1, 0), co-vertices (0, ±5) 12. foci (0, ±4), co-vertices (±4, 0)

13. The decorative arch of a bridge is shaped like an ellipse.

The arch is 120 ft wide and the foci are 48 ft from the

center of the arch. What is the height of the arch?

Find the foci for each equation of an ellipse.

14. 9x2 + 18y2 = 162 15. 25x2 + 16y2 = 1600

Write an equation for each ellipse.

16.

17.

18. Reasoning How are the major and minor axes of an ellipse similar? How are they different?

Prentice Hall Foundations Algebra 2 • Teaching Resources