Equation of an ellipse?

Question

Can anyone help me find an equation of the ellipse with foci (0,12) and (0,-12) and a major axis of lenght 26?

Answer 1

Since the foci are along the y-axis, the major axis of the ellipse will be along the y-axis. Also, the center of the two foci is the center of the ellipse, which will be (0,0) or the origin.

So the only thing left to figure out is the length of the minor axis.

The major axis, minor axis, and focal length (distance from the foci to the center) are related by the Pythagorean theorem:

a² + b² = c²

You know that a = 26/2 = 13, c = 12, so b = 5.

Therefore the equation is:

x²/25 + y²/169 = 1

Answer 2

Here's a hint:

13 squared minus 12 squared is 5 squared.