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The point of the parabola $y = x^{2} + 7 x + 2$ which is closest to the line $y = 3 x - 3$ is

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$(2, 8)$

$(2, - 8)$

$(- 2, 8)$

$(- 2, - 8)$

answer is D.

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Detailed Solution

Differentiating the given curve w.r.t to x
$2 x + 7 = 3 =$ slope of the tangent, here $x = - 2$ put in the given curve, we get $y = - 8$
$∴$ the point is $(- 2, - 8)$

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