Question

If $P$ is a point on the parabola $y=x^2+4$ which is closest to the straight line $y=4x-1,$ then the co-ordinates of $P$ are

• A. $(-2,8)$
• B. $(1,5)$
• C. $(3,13)$
• D. $(2,8)$

Answer 1

The correct option is D $(2,8)$

Tangent at $P$ is parallel to the given line.
$\frac{dy}{dx}{|}_P=4$
$\Rightarrow 2x_1=4$

$\Rightarrow x_1=2$
Required point is $(2,8)$