Question

If $P(x,y)$ is equaidistant from $A(6,2)$ and $B(-2,6)$ then prove that $y=2x$.

Answer 1

Let $(x,y)$ be equidistant point

$\therefore \sqrt{{(x-6)}^2+}{(y-2)}^2=\sqrt{{(x+2)}^2+}{(y-6)}^2$

$\therefore {(x-6)}^2+{(y-2)}^2={(x+2)}^2+{(y-6)}^2$

$\therefore x^2-12x+36+y^2-4g+4=x^2-4x+4+y^2-12y+36$

$\therefore 40-12x-4g=40+4x-12y$

$\therefore 8g=16x$

$y=2x$

$y=2x$