Question

Find the equation of the locus of a moving point such that, the sum of square of its distance from the points (-1, 2) and (-2, 1) is unity.

Answer 1

Answer:

Let (x,y,z) be a point whose locus is to be determined .

According to question ,

Distance of a point from (x,y,z) to (1,-2,2) is 1.

√(x-1)^2 +(y+2)^2 +( z-2)^2 = 1 .

=> (x-1)^2 + (y+2)^2 +(z-2)^2 = 1.

=> x^2-2x +1+y^2+4y +4 +z^2–4z +4=1.

=> x^2+y^2+z^2-2x+4y-4z+8= 0 .