Question

Let A and B be two fixed points, find the locus of the point for which angleAPB is a right angled.

Answer 1

SOLUTION

Let AB= 2a and P(x,y) be a variable point

A=A(-a,0), B=(a,0)

Given, Angle 90°

Then,

AP^2 +PB^2 = AB^2

$= > (x + a) {}^{2} + {y}^{2} + (x - a) {}^{2} + {y}^{2} = (2a) {}^{2} \\ = > 2 {x}^{2} + 2 {y}^{2} + 2 {a}^{2} = 4 {a}^{2} \\ = > {x}^{2} + {y}^{2} = {a}^{2}$

hope it helps ✔️