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

Answer 1

The standard form equation of an ellipse with foci at (0, ±c) and vertices at (0, ±a) is given by:

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

where c^2 = a^2 - b^2

Given that the foci are at (0, ±12) and the vertices are at (0, ±13), we can calculate a and c as follows:

a = 13
c = 12

Now we can substitute the values of a and c into the equation:

(x^2 / 13^2) + (y^2 / b^2) = 1

And since c^2 = a^2 - b^2:

12^2 = 13^2 - b^2
144 = 169 - b^2
b^2 = 169 - 144
b^2 = 25
b = 5

Therefore, the equation of the ellipse is:

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