Question

0 (0,0) A (6,0) B (0,4) are 3 points.
If p is a point such that area of
Angle POB as twice the area of Angle POA,
then
the locus of P Is?​

Answer 1

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MATHS

The co-ordinates of three points O,A,B are (0,0) , (0,4) and (6,0) respectively. a point P moves so that area of triangle POA is always twice the area of triangle POB. Find the equation to both parts of locus of P.

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ANSWER

The three given points are origin, one on x-axis the other on y-axis . Let P be (x,y). We know that are of triangle

=

2

1

base×height

triangle POA = 2 triangle POB

∴

2

1

⋅4x=±2⋅

2

1

⋅6⋅y

or 2x=±6y or x=±3y

Hence the required locus of both the parts is (x−3y)(x+3y)=0