Geometry Helpppp!?

Question

A pair of parallel interstate gas and power lines run 10 meters apart
and are equally distant from relay station A. The power company
needs to locate a gas-monitoring point on one of the lines exactly
12 meters from relay station A. Draw a diagram showing the locus of
possible locations.

Answer 1

Draw the two || lines 10 meters apart. Now draw a third line || to the two lines lying esactly between them .

Any point on this third line is equidistant from station A. So pick a point on the third line and mark it A. Draw a circle with center A and radius 12 meters. The circle will intersect the two parallel lines in 4 points. These four points are the desired locus.

Obviously you could put the point A anywhere on the third line, so actually the locus is the original two parallel lines.