Question

The area of the triangle formed by the intersection of a line parallel to x-axis and passing through $P(h,k)$ with the lines $y=x$ and $x+y=12$ is $4h^2$. If the locus of the point $P$ is $y=\pm Px+Q$, then the value of $P+Q$ is

Answer 1

Area of triangle $=\frac{1}{2}AB.BC=4h^2\therefore AB=2|k-1|=AC\Rightarrow 4h^2=\frac{1}{2}2(k-1{)}^2\Rightarrow \pm 2h=(k-1)$

Locus is $y=2x+1,y=-2x+1$