Mathematics - Point Question with Solution | TestHub

Slope of$\mathrm{P}\mathrm{Q}=\frac{\mathrm{k}-\mathrm{\alpha }}{\mathrm{h}-2\mathrm{\alpha }}=-1$
$k-\alpha =-h+2\alpha$$\Rightarrow \alpha =\frac{h+k}{3} \dots \left(1\right)$
Also,$2h=2\alpha +\beta$and$2k=\alpha +\beta$
$2h=\alpha +2k$$\Rightarrow \alpha =2h-2k \dots \left(2\right)$
From$\left(1\right) \& \left(2\right)$,
$\frac{h+k}{3}=2\left(h-k\right)$
So, locus is$6x-6y=x+y\Rightarrow 5x=7y$.