Mathematics - Parabola Question with Solution | TestHub

$y^1=\frac{x}{2}=m$

$\Rightarrow x=2m\Rightarrow y=m^2$

So equation of tangent is $y-m^2=m(x-2m)$ which passes through $(-1,-1)$ $\begin{array}{rlr}& \Rightarrow -1-m^2=m(-1-2m)& \Rightarrow m^2+m-1=0\Rightarrow m=\frac{-1\pm \sqrt{5}}{2}\end{array}$