# If P is a point on the perabola  $y=x^{2}+4$ which is closest to the straight line $y=4x-1$, then the co-ordinates of P are: Option: 1 (3,13) Option: 2 (2,8) Option: 3 (-2,8) Option: 4 (1,5)

Point P lies on the parabola

If tangent drawn at point P then the distance between P and the given line is the shotest only when the tangent is parallel to the line

Hence slope of the tangent and line is same.

Slope of the line $L_1:\;y=4 x-1$ is $m=4$

$y=x^{2}+4$

$\left.\frac{\mathrm{dy}}{\mathrm{dx}}\right|_{\mathrm{p}}=2x$

$\therefore 2 \mathrm{x}_{1}=4$

$\therefore \text { Point will be }(2,8)$

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