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

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- Mar 2nd 2008, 02:41 PMbrittneyvconic sections
find the equation of the ellipse that goes through the point (2,3) and has foci (2,0) and (-2,0).

- Mar 2nd 2008, 05:14 PMSoroban
Hello, brittneyv!

Quote:

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: .

- Mar 2nd 2008, 07:15 PMbrittneyv
wow thank you so much!