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Question

Equation of the circle passing through the focii 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
Equation of the ellipse is
x216+y29=1a=4, b=3e=1b2a2e=1916e=74

Foci are (±ae,0)(±7,0)
Equation of circle with centre (0,3) and radius r is
x2+(y3)2=r2 (1)
This circle passes throught (7,0)
(7)2+(03)2=r2r2=16
Now, from equation (1)
x2+(y3)2=16x2+y26y7=0

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