Mathematics - Parabola Question with Solution | TestHub

A line passing through $(21,30)$ and normal to the curve $y=2\sqrt{x}$. If $m$ is slope of the normal then $m+6=$ Ans: 1 SOL : 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 $m=-5$ $\therefore m+6=1$