Question

If A(2, 0) and B(0, 3) are two points, find the equation of the locus of point P such that AP = 2BP.

Answer 1

Let P(x, y) be any point on the required locus.
Given, A(2, 0), B(0, 3) and
AP = 2BP
∴ AP² = 4BP²
∴ (x – 2)² + (y – 0)² = 4[(x – 0)² + (y – 3)²]
∴ x² – 4x + 4 + y² = 4(x² + y² – 6y + 9)
∴ x² – 4x + 4 + y² = 4x² + 4y² – 24y + 36
∴ 3x² + 3y² + 4x – 24y + 32 = 0
∴ The required equation of locus is
3x² + 3y² + 4x – 24y + 32 = 0