1.

Suppose A = (-2, 2, 3) and (13, -3, 13). If P is a variable point such that 3PA = 2PB, then find the equation of the locus.

Answer»

Suppose P = (x, y, z).  Now 3PA = 2PB

9PA2 = 4PB2

= 9[(x + 2)2 + (y - 2)2 + (z - 3)2]

= 4[(x - 13)2 + (y + 3)2 + (z - 13)2]

5(x2 + y2 + z2) + 140x - 60y + 50z - 1235 = 0

x2 + y2 + z2 + 28x - 12y + 10z - 247 = 0



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