Question

Find the equation of the curve formed by the set of all points whose distances from the points (3, 4, -5) and (-2, 1, 4) are equal.

Answer 1

Let P(x, y, z) be any point on the given curve, and let A(3, 4, -5) and B(-2, 1, 4) be the given points.

Then, PA=PB

$\Rightarrow P{A}^2=P{B}^2$

$\Rightarrow (x-3{)}^2+(y-4{)}^2+(z+5{)}^2=(x+2{)}^2+(y-1{)}^2+(z-4{)}^2$

$\Rightarrow 10x+6y-18z-29=0$.

Hence, the required curve is 10x+6y-18z-29=0.