Mathematics - Parabola Question with Solution | TestHub

$\mathrm{P}=(1,0)$ $Q=(h,k)$ such that $k^2=8h$ Let $(\alpha ,\beta )$ be the midpoint of PQ $$\begin{array}{rl}& \alpha =\frac{\mathrm{h}+1}{2},\beta =\frac{\mathrm{k}+0}{2}\\ & 2\alpha -1=\mathrm{h},2\beta =\mathrm{k}.\\ & (2\beta {)}^2=8(2\alpha -1)\Rightarrow {\beta }^2=4\alpha -2\\ & \Rightarrow {\mathrm{y}}^2-4\mathrm{x}+2=0.\end{array}$$