Question

Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).

Answer 1

Given , PA = PB

∴ PA² = PB²

⇒ (a - 6)² + (b + 1)² = (a - 5)² + (b - 8)²

⇒ a² + 36 - 12a + b² + 1 + 2b = a² + 25 - 10 a + b² + 64 - 16 b

⇒ -2a + 18b - 52 = 0

⇒ -a + 9b - 26 = 0

⇒ a = 9b - 26