# What is the equation of the ellipse with foci (2, 0), (-2, 0) and vertices (7, 0), (-7, 0)?

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embizze | Certified Educator

The equation for an ellipse is `(x-h)/a^2+(y-k)/b^2=1` where if a>b then the major axis is horizontal with length 2a and minor axis is vertical with length 2b and centered at (h,k). The foci are related to the vertices and co-vertices; if c is the distance from the center to the foci then `a^2-b^2=c^2` .

So this ellipse is centered at the origin (the foci and vertices are symetrically placed about the center.) Since the vertices are at `x=+-7` we have a=7. Since the foci are at `x=+-2` we have c=2.

`49-b^2=4 ==> b=3sqrt(5)` and `b^2=45` .

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The equation is `x^2/49+y^2/45=1`

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The graph: