Find the equation of the set …
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Yogita Ingle 4 years, 5 months ago
Let A(1,2,3)andB(3,2,-1) are the given points and P(x,y,z) is the point that is equidistant from these two points.
Then, PA=√(x-1)2+(y-2)2+(z-3)2
PA=√x2+y2+z2-2x-4y-6z+14
PB=√(x-3)2+(y-2)2+(z+1)2
PB=√x2+y2+z2-6x-4y+2z+14
As, we are given, PA=PB
∴√x2+y2+z2-2x-4y-6z+14
=√x2+y2+z2-6x-4y+2z+14
⇒x2+y2+z2-2x-4y-6z+14
=x2+y2+z2-6x-4y+2z+14
⇒4x=8z
⇒x-2z=0, which is the required equation.
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