Find the equation of the curve formed by the set of all points which are
Question:

Find the equation of the curve formed by the set of all points which are

equidistant from the points A(-1, 2, 3) and B(3, 2, 1).

Solution:

Consider, $C(x, y, z)$ point equidistant from points $A(-1,2,3)$ and $B(3,2,1)$.

∴ AC = BC

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

Squaring both sides,

$(x+1)^{2}+(y-2)^{2}+(z-3)^{2}=(x-3)^{2}+(y-2)^{2}+(z-1)^{2}$

$x^{2}+2 x+1+y^{2}-4 y+4+z^{2}-6 z+9=x^{2}-6 x+9+y^{2}-4 y+4+z^{2}-2 z+1$

$8 x-4 z=0$

Equation of curve is 8x-4z = 0