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

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

Grade:11

1 Answers

Arun
25750 Points
6 years ago
The three given points are O(0,0),A(0,4) and B(6,0) and let P(x,y) be the moving point.
ย Area ofย  trianglePOA=2.Area of triangle POB
1/2 * 4*x = +-2 *1/2 *6 *y
Or x= + 3y andย 
x = -3y
Hence equation of both the parts of locus P is
(x-3y)(x+3y) = 0

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