1.

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).

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 3x+ 3y2 - 8x + 16y + 20 = 0 



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