Hello, brittneyv!

Find the equation of the ellipse that goes through the point

and has foci

The "focus equation" is: .

. . Since , we have: .

The ellipse has the form: .

Since is on the ellipse, we have: .

Substitute [1] into [2]: .

. . which simplifies to: .

Hence: .

Substitute into [1]: .

Therefore, the equation is: .