Question

A = (1,2), B(2,1), and P is any point satisfying the condition PA + PB = 3, then what is the equation of the locus of P?

Answer 1

Let the moving point P be (x, y), then according to the problem, we must have;

PA + PB = 3 or (PA)² = (3 - PB)²

(x - 1)² + (y - 2)² = 9 + {(x - 2)² + (y - 1)²} - 6√(x - 2)² + (y - 1)²} or

6√{(x - 2)² + (y - 1)² = 9 - 2x + 2y. 

Squaring both sides and solving, we get;

32x² + 32y² - 8xy - 108x - 36y + 99 = 0.

It is required locus.