If two lines are parallel, the center of any circle having those two lines as tangents lies on the line equidistant from the two lines. if two lines intersect, the center of any circle having those two lines as tangents lies on one of the two bisectors of the angles the lines make when they intersect.
The slopes of these two lines are and . Because those are not the same the lines are not parallel- but they have the nice property that their product is -1 so the two lines are perpendicular. It also will help to know where the two lines intersect.