1.

Coordinates of the point on the parabola y^(2)=8x which is at minimum distance from the circle x^(2)+(y+6)^(2)=1 is

Answer»

`(2,-4)`
`(2,4)`
`(18,-12)`
None of these

Solution :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`


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