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

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 coordinates of $P$ are

Accepted Answer

Closest point has tangent slope equal to the line's slope: $\dfrac{dy}{dx}=2x_1=4\Rightarrow x_1=2$, $y_1=2^2+4=8$.

$P=(2,8).$

Solutions · 1