The coordinates of the points O, A and B are (0, 0), (0, 4) and (6, 0) respectively. If a points P moves such that the
area of △POA is always twice the area of △POB, then the equation to both parts of the locus of P is
The three given points are O(0, 0), A(0, 4) and B(6, 0) and let P(x, y) be the moving point.
Area of △ POA=2. Area of △ POB
⇒ 12×4×x=±2×12×6×y or x=±3y
Hence the equation to both parts of the locus of P is (x - 3y)(x + 3y) = 0.