Find the equation of the set of all points P(x, y) which is equidistant from (2, -4) and (-1, 5).

Answer 1

(x – 2)^2 + (y + 4)^2 = (x + 1)^2 + (y – 5)^2
x^2 – 4x + y^2 + 8y + 20 = x^2 + 2x + y^2 – 10y + 26
x^2 – 4x + y^2 + 8y + 20 – (y^2 + 8y + 20) = x^2 + 2x + y^2 – 10y + 26 – (y^2 + 8y + 20)
x^2 – 4x – (x^2 + 2x) = x^2 + 2x – 18y + 6 – (x^2 + 2x)
-6x = -18y + 6
(-6x) / (-6) = (-18y + 6) / (-6)
x = 3y – 1
x – 3y + 1 = 0