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Let $0 (0, 0) A (0, 4) B (6, 0)$ let $P$ be moving point, such that the area of triangle $P O A$ is two times the area of triangle $P O B$ then the locus of $P$ will be a straight line whose equation can be

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$x + 3 y = 0$

$x + 2 y = 0$

$2 x - 3 y = 0$

$3 y - x = 0$

answer is A, D.

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Detailed Solution

$Δ P O A = 2$ area of $Δ P O B$

$2 | x | = 6 | y | \Rightarrow x = \pm 3 y$

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