Question

If P(x, y) is a point equidistant from the points A(6, -1) and B (2, 3) show that x - y = 3.

Answer 1

PA = PB

$P{A}^2=PB2$

$(x-6{)}^2+(y+1{)}^2=(x-2{)}^2+(y-3{)}^2$

$x^2$ and $y^2$ will cancel from both sides

then

$36-12x+1+2y=4-4x+9-6y$

$-8x+8y=12-36$

$-8x+8y=-24$

$x-y=3$