The co-ordinates of the points on the barabola `y^(2) =8x`, which is at minium distance from the circle `x^(2) + (y + 6)^(2) = 1` are

Options

A. `(2,-4)`
B. `(2,4)`
C. `(18,-12)`
D. None of these

Answer

D

Explanation

Ellipses centred a origin are given by `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
where a and b are unknown constant.
`(2x)/(a^(2))+(2y)/(b^(2))y_(1)=0implies (x)/(a^(2))+(y)/(b^(2))y_(1)=0`
Differentiating again, we have
`(1)/(a^(2))+(1)/(b^(2))(y_(1)^(2)+yy_(2))=0`
Multiplying `( iii )` with `x` and then subtracting from `( ii )` , we have
`(1//b)^(2)(yy_(1)-xy_(1)^(2)-xyy_(2))=0impliesxyy_(2)+xy_(1)^(2)-yy_(1)=0`