find the equation of the ellipse that goes through the point (2,3) and has foci (2,0) and (-2,0).
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: .