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Question

The equation of circle which passes through focus of parabola x2=4y and touches it at (6,9) is

A
x2+y2+18x28y+27=0
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B
x2+y2+24x27y+26=0
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C
x2+y2+48x12y+11=0
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D
x2+y2+18x22y+21=0
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Solution

The correct option is A x2+y2+18x28y+27=0

dydx(6,9)=2x4=3
Equation of tangent : (y9)=3(x6)
3xy=9
Taking (6,9) as point on circle and line as equation of tangent, using the concept of family of circles
S+λL=0
(x6)2+(y9)2+λ(3xy9)=0 (1)
Required circle passes through (0,1).
36+64+λ(10)=0
λ=10
Putting λ=10 in (1), we get
(x6)2+(y9)2+10(3xy9)=0
x2+y2+18x28y+27=0

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