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The coordinates of a point on the parabo...

The coordinates of a point on the parabola `y^2=8x` whose distance from the circle `x^2+(y+6)^2=1` is minimum is `(2,4)` (b) `(2,-4)` `(18 ,-12)` (d) `(8,8)`

Text Solution

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Distance of point P(x,y) from the focus S(a,0) of the parabola `y^(2)=4ax` is SP = a+x.
Also, given that SP=10.
`:.` 10=2+x
`:.` x=8
So, from `y^(2)=8x`,
`y^(2)=64`
`:. " "y=pm8`
So, coordinates of point P are (8,8) or (8,-8).
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