Mathematics - Parabola Question with Solution | TestHub

Normal at $\left({\mathrm{at}}^2,2\mathrm{at}\right)$ is $\mathrm{y}+\mathrm{tx}=2\mathrm{at}+{\mathrm{at}}^3\left(a=\frac{1}{4}\right)$

If this passes through $(\mathrm{c},0)$

We have $ct=2at+a{t}^3=\frac{t}{2}+\frac{t^3}{4}$

$\Rightarrow \mathrm{t}=0$ or ${\mathrm{t}}^2=4c-2$ If $t=0$, the point at which the normal is drawn is $(0,0)$

if $t\ne 0$, then the two values of $t$ represents slope of normals through $(\mathrm{c},0)$