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Question

The equation of the circle whose end points of the diameter are the foci of the ellipse x216+y27=1 is

A
x2+y2=16
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B
x2+y2=23
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C
x2+y2=7
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D
x2+y2=9
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Solution

The correct option is D x2+y2=9
Given ellipse: x216+y27=1
Comparing this with
x2a2+y2b2=1
We get
a=4,b=7e=1b2a2e=1716e=34

Foci =(±ae,0)=(±3,0)
Now, the equation of the circle in diametric form is
(x+3)(x3)+(y0)(y0)=0x2+y2=9

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