The locus of a point which moves in such a way that its distance from the line is…

MATHEMATICS · Single correct · CBSE · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

The locus of a point which moves in such a way that its distance from the line

\frac{x}{1} = \frac{y}{1} = \frac{z}{-1}

is twice the distance from the plane

x + y + z = 0

is (1)

x^2 + y^2 + z^2 - 5x - 3y - 3z = 0

(2)

x^2 + y^2 + z^2 + 5x + 3y + 3z = 0

(3)

x^2 + y^2 + z^2 - 5xy - 3yz - 3zx = 0

(4)

x^2 + y^2 + z^2 + 5xy + 3yz + 3zx = 0