Mathematics - Application of Derivative Question with Solution | TestHub

Equation of normal to parabola
$y^2=8x\text{ is }y=mx-4m-2m^3$
passes through $(0,-6)$ we get
$\begin{array}{rl}& -6=-4\mathrm{m}-2{\mathrm{m}}^3\\ & \Rightarrow {\mathrm{m}}^3+2\mathrm{m}-3=0\\ & \Rightarrow (\mathrm{m}-1)\left({\mathrm{m}}^2+\mathrm{m}+3\right)=0\Rightarrow \mathrm{m}=-1\\ & \mathrm{P}=\left({\mathrm{am}}^2,-2\mathrm{am}\right)=(2,-4)\\ & \therefore \text{ Shortest distance }=\mathrm{PC}-\mathrm{r}\\ & =(2\sqrt{2}-1)\end{array}$