Question

Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).

Answer 1

Let P(x,y). A(6, - 1) and b(2, 3) be the given points.
Since PA = PB
So `sqrt(( x - 6)^2 + (y + 1)^2) = sqrt((x - 2)^2 + (y - 3)^2)`
Squaring both sides
x² + 36 - 12x + y² + 1 + 2y = x² + 4 - 4x + y² + 9 - 6y
⇒ -8x + 8y = 13 - 36 - 1
⇒ -8(x - y) = -24
⇒x - y = 3.