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Question

Find the equation of the ellipse whose vertices are (±6,0) and foci are (±4,0)

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Solution

Since the foci of the ellipse are F1(4,0) and F2(4,0) which lie on the xaxis and the mid-point of the line segment F1F2 is (0,0),, origin is the centre of the ellipse and the major axis lies along xaxis.

Hence the equation of the ellipse can be taken as
x2a2+y2b2=1 .........(1)

As the vertices are (±6,0).So,a=6

Also,c=4

We know that b2=a2c2=6242=3616=20

From equation (1), the equation of the ellipse is x236+y220=1

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