find the locus of a point P which moves in such a way that 2PA=3PB, where A(-2,1,3) and B(3,-1,2) are the given points.

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Please find below the solution to the asked query:

Let Ph,k,j be the required point on the locus.Now, A-2,1,3 and B3,-1,2 are the given points.PA=h+22+k-12+j-32       Using distance between two points formulaPB=h-32+k+12+j-222PA=3PB2h+22+k-12+j-32=3h-32+k+12+j-224h+22+k-12+j-32=9h-32+k+12+j-224h2+16+16h+4k2+4-8k+4j2+36-24j=9h2+81-54h+9k2+9+18k+9j2+36-36j5h2+5k2+5j2-70h+26k-12j+70=0Locus of P is , 5x2+5y2+5z2-70x+26y-12z+70=0

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