Question

find the equation of locus of a point which moves so that its distance from the point(-2,1,3)is twice its distance from XY plane​

Answer 1

The equation of locus of a point which moves so that its distance from the point(-2,1,3)is twice its distance from XY plane is x²+y²-3z²+4x-2y-6z+14=0.

• ​The distance of the point (x,y,z) from (-2,1,3) is given by  $\sqrt{(x+2)^{2}+(y-1)^{2}+(z-3)^{2} }$
• The distance of a point (x,y,z) from the XY plane will be equal to its z-coordinate.

• So all the points(x,y,z) that satisfies the relation $\sqrt{(x+2)^{2}+(y-1)^{2}+(z-3)^{2} }$ = 2z , will be the part of the locus.
• The answer is obtained by squaring the above equation and rearranging the terms.