Question

FIND THE EQUATION OF THE ELLIPSE WITH A CENTER AT (2, 2), VERTICES AT (-3,

2) AND (7, 2), AND FOCI AT (-1, 2) AND (5,2),

Answer 1

Explanation:

The standard equation of an ellipse centered at the point (h,k) is

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

where a is the distance from the center to one of the vertex. We have the relation
`c= \sqrt[]{a^2-b^2}` where c is the distance from one of the focus to the center.

The distance between one vertex and the center is 5. So a=5. The distance from one focue to the center is 3. Then c =3. So we have that
`b^2 = a^2-c^2 = 16`

so the equation is

`((x-2)^2)/(25)+((y-2)^2)/(16) = 1`