Mathematics - Parabola Question with Solution | TestHub

Normal to $y^2=4x$, is $y-mx-2m-m^3$ which passes through $(9,6)$. Now, $6=9m-2m-m^3$ $\Rightarrow m^3-7m+6=0\Rightarrow m=1,2,-3$ $\therefore$ Equation of normals are $y-x+3=0$ $y+3x-33=0$ and $y-2x+12=0$