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Find the equation of the locus of a point P which moves such that its distance from the origin is twice its distance from the point A(1,2). |
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Answer» We have OP = 2PA (OP)2 = 4(PA)2 x2 + y2 = 4[(x - 1)2 + (y - 2)2] x2 + y2 = 4x2 + 4y2 - 8x - 16y + 20 3x2 + 3y2 - 8x - 16y + 20 = 0 Hence, the equation of the locus is 3x2 + 3y2 - 8x + 16y + 20 = 0 |
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