Question

A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA² – PB² = 13.

Answer 1

Let P(x, y) be any point on the required locus.
Given, A(2, 4), B(5, 8) and
PA² – PB² = 13
∴ [(x – 2)² + (y –  4)²] –  [(x –  5)² + (y –  8)²] = 13
∴ (x² –  4x + 4 + y² –  8y + 16) –  (x² –  10x + 25 + y² –  16y + 64) = 13
∴ 6x + 8y –  69 = 13
∴ 6x + 8y –  82 = 0
∴ 3x + 4y –  41 = 0
∴ The required equation of locus is
3x + 4y –  41 = 0.