Write an equation of the ellipse with foci at (0,+12) and vertices at (0,+13)

To solve this problem you must apply the proccedure shown below:

1. You have that the ellipse given as a vertical major axis (a=13), therefore, taking the ellipse with its center at the origin, you have the following equation:

(y^2/a^2) + (x^2/b^2) = 1

2. You have the distance from the center of the ellipse to the focus:

c=12, therefore, you can calculate the value of b, the minor radius:

c^2=a^2-b^2

b=√ (13^3-12^2)

b=5

3. Therefore, the equation is:

a^2=169

b^2=25

(y^2/169) + (x^2/25) = 1

The answer is: (y^2/169) + (x^2/25) = 1