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The coordinates of the point on the para...

The coordinates of the point on the parabola `y^2=8x` which is at a minimum distance from the circle `x^2+(y+6)^2=1` are

A

(2,4)

B

`(2,-4)`

C

`(-2,4)`

D

none of these

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The correct Answer is:
B
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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

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