Question

Let A (2,5) and B(4,9) be two given process find the locus of a point p moving such that $\angle APB={90}^o$

Answer 1

Let $P(x,y)$ slope of $AP\frac{y-5}{x-2}$, $BP=\frac{y-9}{x-4}$

As $AP\perp BP\Rightarrow \left(\frac{y-5}{x-2}\right)\left(\frac{y-9}{x-4}\right)=-1\Rightarrow \frac{y^2-14y+45}{x^2-6x+8}=-1$

$\Rightarrow y^2-14y+45=-x^2+6x-8\Rightarrow x^2+y^2-14y-6x+53=0$