What is the locus of points in a plane equidistant from two parallel lines and a given distance d from point p

What is the locus of points in a plane equidistant from two parallel lines and a given distance d from a point P? Sketch all solutions.What is the locus of points in a plane equidistant from two parallel lines and a given distance d from point pTake it one part at a time. The first condition describes a third line parallel to and halfway between the other two lines. The second condition is where that line intersects a circle centered at P with radius d. This could be 0, 1 or 2 points, depending on where P is and how large d is.