Answer:
Step-by-step explanation:
The standard equation of an ellipse centered at the point (h,k) is
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1[/tex]
where a is the distance from the center to one of the vertex. We have the relation [tex]c= \sqrt[]{a^2-b^2}[/tex] 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 [tex]b^2 = a^2-c^2 = 16[/tex]
so the equation is
[tex]\frac{(x-2)^2}{25}+\frac{(y-2)^2}{16} = 1[/tex]
