Question

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 $\Delta POA$is always twice the area of $\Delta POB$, then the equation to both parts of the locus of P is.

• A. $(x - 3y)(x + 3y) = 0$
• B. $(x - 3y)(x + y) = 0$
• C. $(3x - y)(3x + y) = 0$
• D. None of these

Answer 1

Answer: (A)

$(x - 3y)(x + 3y) = 0$

Answer 2

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 $\triangle P O A = 2$Area of $\triangle P O B$

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

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