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Question

Let the equation of an ellipse be x2144+y225=1. Then, the radius of the circle with centre (0,2) and passing through the foci of the ellipse is :

A
9
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B
7
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C
11
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D
5
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Solution

The correct option is C 11
Given equation of ellipse is
x2144+y225=1
Here, a2=144 and b2=25
Now, e=1b2a2=125144
=119144=11912
Foci of an ellipse =(±ae,0)
=(±12×11912,0)
=(±119,0)
Since, the circle with centre (0,2) and passing through foci (±119,0) of the ellipse.
Radius of circle =(1190)2+(02)2
=119+2=121=11

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