Question

write the equation of the ellipse using the given information: the ellipse has foci (0,3) and (0,-3) and major vertices (0,5) and (0,-5).

Answer 1

Answer: (x^2)/16 + (y^2)/25 = 1

Explanation:

According to the problem we can figure out that the center of the ellipse is (0,0).

Since the foci is (0,3) and (0,-3) we know that the value of c is 3. The major vertices are (0,5) and (0,-5) so the value of a is 5.

If we put this into the equation a^2=b^2 + c^2, we get 25=9+ b^2

We get b^2 is 16

Now since we know that the ellipse is vertical because the x value didn’t change, we know that the b^2 value comes first in the equation. Then the a^2 value which is 25.