The pedal of a curve
with respect to a point
is the locus of the foot of the perpendicular
from to the tangent
to the curve. More precisely, given a curve , the pedal curve of
with respect to a fixed point (called the pedal point) is
the locus of the point
of intersection of the perpendicular from to a tangent
to . The parametric equations for a curve
relative to the pedal
point
are given by
(1)
(2)
If a curve
is the pedal curve of a curve , then is the negative pedal curve
of (Lawrence 1972, pp. 47-48).
When a closed curve rolls on a straight line, the area between the line and roulette
after a complete revolution by any point on the curve is twice the area
of the pedal curve (taken with respect to the generating point) of the rolling curve.
with respect to a point 
is the locus of the foot of the perpendicular
from 
to the tangent
to the curve. More precisely, given a curve 
, the pedal curve 
of 
with respect to a fixed point 
(called the pedal point) is
the locus of the point 
of intersection of the perpendicular from 
to a tangent
to 
. The parametric equations for a curve
relative to the pedal
point 
are given by
is the pedal curve of a curve 
, then 
is the negative pedal curve
of 
(Lawrence 1972, pp. 47-48).
