Question

The locus of the point which moves in such a way that its distance from the line $y=-6$ is always equal to 1 unit is

Answer 1

The line $y=-6$ is parallel to the x-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 $y=-6$ is always equal to 1 unit is a pair of lines parallel to $y=-6$, at a distance of 1 unit from it.

Take points P and Q on y-axis, which are at a distance of 1 unit from the point where the line $y=-6$ touches the y-axis, i.e. A.

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

Thus the locus of the point which moves in such a way that its distance from the line $y=-6$ is always equal to 1 unit are the lines $y=-5$ and $y=-7$.