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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 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 trianglePOA=2.Area of triangle POB1/2 * 4*x = +-2 *1/2 *6 *yOr x= + 3y and x = -3yHence equation of both the parts of locus P is(x-3y)(x+3y) = 0
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