Practice!

Sample Problem

Find the standard form of the equation of the ellipse (centered at the origin) with vertices (0, ±6) and foci at (0, ±2).

Solution

If the center of the ellipse is at the origin (0,0) and the foci (0, ±2) lie on the major axis (which in this case is vertical), then the equation takes the form:

 0) to one of the foci (0, ±2) is c=2. Because the two vertices of the ellipse are (0,±6), we also know that the major axis has a length of 12 [from (0, -6) to (0, 6)], that is 2a=12 → a=6.

c2=a2-b2

(2)2=(6)2-b2

b2=32

b=√32

The equation of this ellipse is therefore