Question

The locus of the point which moves in such a way that its distance from the line $x=6$ is always equal to 2 units is

• A. the line $x=4$.
• B. the line $x=8$.
• C. y-axis.
• D. lines $x=4$ and $x=8$.

Answer 1

The correct option is D

lines $x=4$ and $x=8$.

The line $x=6$ is parallel to the y-axis.

We know that the locus of a point which is at a given distance from a given line, is a pair of lines parallel to the given line and at a given distance from it.

Thus, the locus of the point which moves in such a way that its distance from the line $x=6$ is always equal to 2 units is a pair of lines parallel to $x=6$, at a distance of 2 units from it.

Take points P and Q on x-axis, which are at a distance of 2 units from the point where the line $x=6$ touches the x-axis, i.e. A.

Draw lines m and n from P and Q, parallel to the line $x=6$.

Thus the locus of the point which moves in such a way that its distance from the line $x=6$ is always equal to 2 units are the lines $x=4$ and $x=8$.