The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are
Let P (2t2, 4t) be any point on the parabola. The centre of the given circle is O (0, –6) and the radius is 1.
(other roots are imaginary)
Hence OP2 is minimum at t = –1. But if A is any point on the circle and onOP (min), then AP will be minimum when OP is minimum as AP = OP – (radius of circle). Thus the required point is P(2(–1))2, 4(–1) = (2, –4).