PEDAL CURVE : Summary

If you have worked through the pedal curve constructions, you will have discovered the results in the following table. We have only listed the cases where the pedal curve is known or of interest.

CURVES AND THEIR PEDAL CURVES
Original curve 
Pedal point
Pedal curve

Astroid
Centre
Quadrifolium 

Cardioid
Cusp 
Cayley’s sextic 

Circle
Any point not at centre
Limaçon

Circle
On circle
Cardioid

Deltoid
 Cusp
Simple folium 

Deltoid
Vertex
Regular bifolium

Deltoid
Centre
Trifolium

Ellipse
Focus
Circle 

Hyperbola
Focus
Circle  

Rectangular hyperbola
Centre
Lemniscate

Parabola
Focus 
Line 

Parabola
Vertex 
Cissoid 

Parabola
Intersection of directrix and axis
Right strophoid

Parabola
Reflection of focus in directrix
Trisectrix of Maclaurin