Let P be a point on parabola ` x ^ 2 = 4y ` . If the distance of P from the centre of circle ` x ^ 2 + y ^ 2 + 6x + 8 = 0 ` is minimum, then the equation of tangent at P on parabola ` x ^ 2 = 4y ` is :

Equation of tangent to the parabola y^(2)=16x at P(3,6) is

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 y + 12 = 0 x^ 2 + y^ 2 − x/ 4 + 2 y − 24 = 0 x^ 3 + y^ 2 − 4 x + 9 y − 18 = 0 x^ 2 + y^ 2 − 4 x + 8 y + 12 = 0

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

Let P be the point on the parabola y^(2) = 4x which is at the shortest distance from the centre S of the circle x^(2) + y^(2) - 4x - 16y + 64 = 0 . Let Q be the point on the circle dividing the lie segment SP internally. Then