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  4. The equation of locus of a point whose distance from the y-axis is equal to its distance from the point (2, 1, -1) is

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Q. The equation of locus of a point whose distance from the y-axis is equal to its distance from the point (2, 1, -1) is

Introduction to Three Dimensional Geometry

Solution:

The variable point is P (x, y, z).
Its distance from the y-axis = $\sqrt{x^2 + z^2}$
Its distance from (2, 1, -1)
$\sqrt{\left(x-2\right)^{2} +\left(y-1\right)^{2}+\left(z+1\right)^{2}}$
Given
$ \sqrt{x^{2}+z^{2}} = \sqrt{\left(x-2\right)^{2}+\left(y-1\right)^{2}+\left(z+1\right)^{2}} $
$\Rightarrow y^{2} -2y-4x+2z+6=0 $