if A (-2,2,3) and B(13,-3,13) are two points find the locus of a point P which moves in a such - Maths - Introduction to Three Dimensional Geometry

Question

if A (-2,2,3) and B(13,-3,13) are two points find the locus of a
point P which moves in a such a way that 3PA=2PB

Rajat Sethi · Accepted Answer

Given points are A(-2,2,3) and B = (13,-3,13)Let P(x,y,z) be any
points on the locus 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]⇒9(x2+4x+4+y2-4y+4+z2-6z+9)=4(x2-26x+169+y2+6y+9+z2-26z+169)⇒5x2+5y2+5z2+140x-60y+50z-1235=0⇒x2+y2+z2+28x-12y+10z-247=0Locus
of P is x2+y2+z2+28x-12y+10z-247=0

if A (-2,2,3) and B(13,-3,13) are two points.find the locus of a point P which moves in a such a way that 3PA=2PB.