Question
Let P be the point on the parabola, y2=8x which is at a minimum distance from the centre C of the circle, x2+(y+6)2=1. Then the equation of the circle, passing through C and having its centre at P is:
-
x2+y2−4x+8y+12=0
-
x2+y2−x+4y−12=0
-
x2+y2− 4 x +2y−24=0
-
x2+y2−4x+9y+18=0
Solution
A.
x2+y2−4x+8y+12=0
Centre of circle x2 + (y+6)2 = 1 is C (0,6)
Let the coordinates of point P be (2t2, 4t)
Now, let 
