The equation of circle which passes through focus of parabola x2=4y and touches it at (6,9) is
A
x2+y2+18x−28y+27=0
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B
x2+y2+24x−27y+26=0
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C
x2+y2+48x−12y+11=0
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D
x2+y2+18x−22y+21=0
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Solution
The correct option is Ax2+y2+18x−28y+27=0
dydx∣∣∣(6,9)=2x4=3
Equation of tangent : (y−9)=3(x−6) ⇒3x−y=9
Taking (6,9) as point on circle and line as equation of tangent, using the concept of family of circles S+λL=0 ⇒(x−6)2+(y−9)2+λ(3x−y−9)=0⋯(1)
Required circle passes through (0,1). ∴36+64+λ(−10)=0 ⇒λ=10
Putting λ=10 in (1), we get (x−6)2+(y−9)2+10(3x−y−9)=0 ⇒x2+y2+18x−28y+27=0