QJEEM24Mabbb8: JEE Main 2024 Mathematics - Class 11 JEEM24Mabbb8 Solution: If the shortest distance of the parabola from the centre of the …

Equation of normal to parabola

$\mathrm{y=m x-2 m-m^3}$

this normal passing through center of circle $(2,8)$

$\begin{aligned}& 8=2 \mathrm{~m}-2 \mathrm{~m}-\mathrm{m}^3 \\& \mathrm{~m}=-2\end{aligned}$

So point $\mathrm{P}$ on parabola $\Rightarrow\left(\mathrm{am}^2,-2 \mathrm{am}\right)=(4,4)$

And $\mathrm{C}=(2,8)$

$\begin{aligned}& \mathrm{PC}=\sqrt{4+16}=\sqrt{20} \\& \mathrm{~d}^2=20\end{aligned}$