Question

If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.

Answer 1

Let P(x, y) be any point on the required locus.
Given, A(1, 3) and B(2, 1).
PA = PB
∴ PA² = PB²
∴ (x – 1)² + (y – 3)² = (x – 2)² + (y – 1)²
∴  x² –  2x + 1 + y² –  6y + 9 = x² –  4x + 4 + y² –  2y + 1
∴  –2x – 6y + 10 = –4x – 2y + 5
∴ 2x – 4y + 5 = 0
∴ The required equation of locus is 2x – 4y + 5 = 0.