Question

The coordinates of the points O, A and B are (0, 0), (0, 4) and (6, 0) respectively. If a point P moves such that the

area of $△$POA is always twice the area of $△$POB, then the equation to the locus of P is

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

The three given points are O(0, 0), A(0, 4) and B(6, 0) and let P(x, y) be the moving point.

$Areaof△POA=2.Areaof△POB$

$\Rightarrow$ $\frac{1}{2}\times 4\times x=\pm 2\times \frac{1}{2}\times 6\times yorx=\pm 3y$

Hence the equation to both parts of the locus of P is (x - 3y)(x + 3y) = 0.