Mathematics - Parabola Question with Solution | TestHub

$(y-x-1{)}^2=4x\Rightarrow x^2-2xy+y^2-2x-2y+1=0$ $\Rightarrow (\mathrm{x}-\mathrm{y}+\lambda {)}^2=2\mathrm{x}+2\mathrm{y}-1+2\lambda \mathrm{x}-2\lambda \mathrm{y}+{\lambda }^2,\lambda \in \mathrm{R}$ we choose $\lambda$ such that $x-y+\lambda =0$ and $2x+2y-1+2\lambda x-2\lambda y+{\lambda }^2=0$ are perpendicular lines $\Rightarrow \lambda =0$ now solve it.