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