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Question

The equation of the circle passing through the foci of the ellipse x216+y29=1, and having centre at (0,3) is

A
x2+y26y7=0
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B
x2+y26y+7=0
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C
x2+y26y5=0
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D
x2+y26y+5=0
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Solution

The correct option is A x2+y26y7=0
The equation of the ellipse is
x216+y29=1
So, c=±a2b2
=169
c=±7

radius of circle, r=OF
=(30)2+(07)2
=4
Equation of circle having centre (0,3) and radius 4 is
(x0)2+(y3)2=42
x2+y26y7=0

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