Mathematics - Parabola Question with Solution | TestHub

Let $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ be a point on ${\mathrm{y}}^2=-8(\mathrm{x}+4)$ equation of chord of contact is $2\mathrm{x}-{\mathrm{y}}_1\mathrm{y}+2{\mathrm{x}}_1=0$, if $\mathrm{p}(\mathrm{h},\mathrm{k})$ be its mid point, then its equation will be $2\mathrm{x}-\mathrm{ky}+{\mathrm{k}}^2-2\mathrm{h}=0$ Compare both $\mathrm{k}={\mathrm{y}}_1,2{\mathrm{x}}_1={\mathrm{k}}^2-2\mathrm{h}$ So, ${\mathrm{k}}^2=-4\left({\mathrm{k}}^2-2\mathrm{h}+8\right)\Rightarrow {\mathrm{k}}^2=\frac{8}{5}(\mathrm{h}-4)$ So, $\lambda =\frac{8}{5}$