# 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 : Option 1)  x2 + y2 − 4x + 8y + 12 = 0   Option 2) x2+y2−x+4y−12=0   Option 3)   Option 4) x2 + y2 − 4x + 9y + 18 = 0

As we learnt in

Parametric coordinates of parabola -

- wherein

For the parabola.

Equation of a circle -

- wherein

Circle with centre and radius .

Equation of  normal of in

parametric form

If it passes through (0,-6)

Put a=2

we get t= -1

This point is (a, -2a)    (2, -4)

Radius of circle = distance between   and

Hence equation is

Option 1)

x2 + y2 − 4x + 8y + 12 = 0

Correct option

Option 2)

x2+y2−x+4y−12=0

Incorrect Option

Option 3)

Incorrect Option

Option 4)

x2 + y2 − 4x + 9y + 18 = 0

Incorrect Option

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