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Question

Find the equation for the ellipse that satisfies the given conditions:
Vertices (±6,0), foci (±4,0).

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Solution

It is given that, vertices (±6,0), foci (±4,0)
Clearly, the vertices are on the x-axis.
Therefore, the equation of the ellipse will be of the form x2a2+y2b2=1, where a is the semi-major axis.
Also, a=6,ae=4e=23
We know that b2=a2(1e2)=a2a2e2=3616=20
Thus, the equation of the ellipse is x236+y220=1

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