Mathematics - Parabola Question with Solution | TestHub

Hint: Any point on the parabola is $\left(x,x^2+7x+2\right)$

Its distance from the line $y=3x-3$ is given by

$P=\left|\frac{3x-\left(x^2+7x+2\right)-3}{\sqrt{9+1}}\right|=\left|\frac{x^2+4x+5}{\sqrt{10}}\right|=\frac{x^2+4x+5}{\sqrt{10}}($ as $x^2+4x+5>0\forall x\in R)$ $\frac{dp}{dx}=0\Rightarrow x=-2$ the required point $=(-2,-8)$