Find the locus of the points which are 3 units away from the line 5x-12y-7=0.

What they are asking for is the equation of the two lines which will be 3 units from the given line.

You can use the distance formula or the formula for the distance from a point to a line.

To use the distance from a point to a line formula, just let x=0 and set it equal to 3 and solve for y.

\frac{|Ax+By+C|}{\sqrt{A^{2}+B^{2}}}

\frac{|5(0)-12y-7|}{\sqrt{(5)^{2}+(-12)^{2}}}=3

Solve for y. You will get two solutions. One for each line on either side of the given line.

Your given line has slope 5/12, so you know the other two lines will have the same slope.