a plane curve generated by the loci of points p and pprime; on a straight line that intersects the y-axis at a point n and the minus x-axis at a fixed point q, such that pn = npprime; = on, as on changes, where o is the origin. Equation: y^{2} = x^{2} (x + a)/(a − x).
The curve traced out by points P and P' which lie on lines through a fixed point A where the midpoint M of PP' is on a fixed line and the absolute value |PM| equals the absolute value |P'M| equals the absolute value |MO|, where O is the projection of A onto that fixed line.