Mathematics - Parabola Question with Solution | TestHub

Equation of the normal is $y=mx-2m-m^3$

If it pass through $(21,30)$ we have $30=21m-2m-m^3\Rightarrow m^3-19m+30=0$

Then $m=-5,2,3$

But if $m=2$ or 3 then the point where the normal meets the curve will be $\left(a{m}^2,-2am\right)$

where the curve does not exist. Therefore $m=-5$

$\therefore m+6=1$