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:

(C) x² + y² - 4x + 8y + 12 = 0

(A) x² + y² - x/4 + 2y - 24 = 0

(B) x² + y² - 4x + 9y + 18 = 0

(D) x² + y² - x + 4y - 12 = 0

Coordinate Geometry: JEE Main 2016 Mathematics question

JEE Main 2016 · Session, Shift 1 · Q4703

JEE Main 2016Session, Shift 1MathematicsMediumCoordinate Geometry478× since 2002

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} + {\left( {y + 6} \right)^2} = 1

. Then the equation of the circle, passing through

C

and having its centre at

P

is: