Question

The line segment joining $(2,-1)$ and $(-2,1)$ subtends a right angle at $P$. The locus of $P$ is ........

Answer 1

Given the two points $(2,-1)$ and $(-2,1)$

Let the coordinate of P be $(x,y)$

$\therefore slope=\frac{y-3}{x-2}\times \frac{y-5}{x+1}=-1$

$y^2-8y+15+x^2-x-2=0{(x-\frac{1}{2})}^2+(y-4{)}^2=\frac{9}{4}$