Question

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

Answer 1

Answer:

Step-by-step explanation:

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

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1$

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

$\frac{(x-2)^2}{25}+\frac{(y-2)^2}{16} = 1$