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Let 0-=(0,0),A-=(0,4),B-=(6,0)dot Let P ...

Let `0-=(0,0),A-=(0,4),B-=(6,0)dot` Let `P` be a moving point such that the area of triangle `P O A` is two times the area of triangle `P O B` . The locus of `P` will be a straight line whose equation can be `x+3y=0` (b) `x+2y=0` `2x-3y=0` (d) `3y-x=0`

A

`x+3y=0`

B

`x+2y=0`

C

`2x-3y=0`

D

`3y-x=0`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Let point P be (x,y).
`arDeltaPOA=(1)/(2)(OA)|x|=2|x|`
`arDelta POA =(1)/(2)(OB)|y|=3|y|`
`therefore2|x|=6|y|`
or `|x|=3|y|` or `3y-x=0 or 3y+x0`
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