If the shortest distance of the parabola y^2=4x from the centre of the circle x^2+y^2-4x-16y+64=0 is d, then d^2 is equal to : (1) 16 (2) 24 (3) 20 (4) 36

Ans. (3)
Sol. Equation of normal to parabola
y=mx-2m-m^3
this normal passing through center of circle (2,8)
8=2m-2m-m^3
or, m=-2
So point P on parabola ⇒(am^2,-2am)=(4,4)
And C=(2,8)
PC=√(4+16)=√20
d^2=20