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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

The foci (±4,0) lie on x - axis.
So the equation of ellipse in standard form is,
x2a2+y2b2=1
Now vertices(±a,0)is(±6,0)a=6Foci(±c,0)is(±4,0)c=4We know that c2=a2b2(4)2=(6)2(b)2b2=3616=20Thus equation of required ellipse is ,x236+y220=1


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