Negative pedal curve
In geometry, a negative pedal curve is a plane curve that can be constructed from another plane curve "C" and a fixed point "P" on that curve. For each point "X" ≠ "P" on the curve "C", the negative pedal curve has a tangent that passes through "X" and is perpendicular to line "XP". Constructing the negative pedal curve is the inverse operation to constructing a pedal curve. Definition. In the plane, for every point "X" other than "P" there is a unique line through "X" perpendicular to "XP". For a given curve in the plane and  a given fixed point "P", called the pedal point, the negative pedal curve is the envelope of the lines "XP" for which "X" lies on the given curve. Parameterization. For a parametrically defined curve, its negative pedal curve with pedal point (0; 0) is defined as Properties. The negative pedal curve of a pedal curve with the same pedal point is the original curve.