Let P be the point on the parabola, y^{2} = 8x which is at a minimum distance from the centre C of the circle, x^{2} + (y + 6)^{2} = 1. Then the equation of the circle, passing through C and having its centre at P is:

- x
^{2}+ y^{2}– x/4 + 2y – 24 = 0 - x
^{2}+ y^{2}– 4x + 8y + 12 = 0 - x
^{2}+ y^{2}– 4x + 9y + 18 = 0 - x
^{2}+ y^{2}– x + 4y – 12 = 0

**Answer**

For minimum distance from the centre of circle to the parabola at point P, the line must be normal to the parabola at P.

Let P(at^{2}, 2at) = (2t^{2}, 4t)

y = –tx + 4t + 2t^{3}

–6 = 4t + 2t^{3}

t = –1

Equation of required circle:

(x – 2)^{2} + (y + 4)^{2} = 8

**The correct option is B.**