Find the coordinates of a point on the parabola `y=x^2+7x+2` which is closest to the straight line `y=3x-3.`

Explanation

Let the coordinates of the required point of the parabola `y=x^{2}+7 x+2` be `(h, k)`.


`therefore k=h^{2}+7 h+2 quad ldots . .(1)`


Distance of the point ( `h`, `k` ) from the straight line `y=3 x-3` is given by


`D=frac{|3 h-k-3|}{sqrt{(3)^{2}+(-1)^{2}}}=frac{|3 h-k-3|}{sqrt{10}} ldots . .(2)`


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