Question

The equation of the circle which passes through the focus of the parabola $x^2=4y$ and touches it at (6, 9) is

• A. $x^2+y^2+18x+28y+27=0$
• B. $x^2+y^2+18x-28y+27=0$
• C. $x^2+y^2+18x-28y=0$
• D. $x^2+y^2+18x+27=0$

Answer 1

The correct option is B $x^2+y^2+18x-28y+27=0$

$x^2+y^2+2gx+2fy+c=0$
It passes through (0, 1)
1 + 2f + c = 0 ....(i)
36 + 81 + 12g + 18f + c = 0 ....(ii)
Equation of tangent at (6, 9)
$3x-y=9$
$\frac{9+f}{6+g}=-\frac{1}{3}$ ...(iii)
$\therefore$ Required equation
$x^2+y^2+18x-28y+27=0$