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)

Answers (1)

 

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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