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Question

If the latus rectum of an ellipse with axis along x-axis and centre at origin is 10, distance between foci = length of minor axis, then the equation of the ellipse is ...... .

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Solution

2b2a=10

2ae=2b
b=ae
We know, b2=a2(1e2)
2a2e2=a2
e=12
Thus, a=b2
2b2a=10
b=52
a=10
Therefore, the required equation of the ellipse is
x2100+y250=1

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