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Question

The equation of the circle passing through the foci of the ellipse
x29+y216=1 and having the 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


We have, equation of ellipse as x29+y216=1.
Here, a = 4, b = 3
So, e=1916=74
Foci of the ellipse are:(±ae,0)=(±4×74,0)=(±7,0)
Radius of the circle is the distance between the centre of the circle and point on the circle.
So, r=(7)2+32=7+9=16=4
So, the equation of the circle is
(x0)2+(y3)2=16
x2+y26y7=0


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