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Question

Find the equation of the ellipse whose foci are (0,±6) and length of the minor axis is 16

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Solution

Since the foci of the ellipse are F1(0,6) and F2(0,6) which lie on the yaxis 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 yaxis.

Hence the equation of the ellipse can be taken as

x2b2+y2a2=1 .........(1)

Here c=6

Also, the length of the minor axis is 16

2b=16

b=162=8

We know that b2=a2c2

82=a262

a2=64+36=100

From (1) , the equation of the ellipse is x264+y2100=1

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