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
