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 

∴ x² – 4x+ y² – 8y + 20 – x² + 10x – y² + 16y – 89 = 13 

∴ 6x + 8y- 69 = 13 

∴ 6x + 8y – 82 = 0 

∴ 3x + 4y – 41 = 0 

∴ The required equation of locus is 3x + 4y-41 = 0.