Question

$A(2,0)$ and $B(-2,0)$ are two given points. Find the equation of locus of point $P$ , such that $\angle APB$ is a right angle.

Answer 1

$A(2,0)$ $B(-2,0)$

Let $P(x,y)$

Since $\angle APB$ is right angle, $P$ could be any point on the circle with $AB$ as a diameter.

Hence equation of circle with $AB$ as a diameter is

$(x-2)(x-(-2\left)\right)+(y-0)(y-0)=0$

$x^2-4+y^2=0$

( or ) $x^2+y^2=4$ is the equation of the locus of point $P$.