the pedal curve results from the orthogonal projection of a fixed point on the tangent lines of a given curve. more precisely, for a plane curve "c" and a given fixed "pedal point" "p", the pedal curve of "c" is the locus of points "x" so that the line "px" is perpendicular to a tangent "t" to the curve passing through the point "x". conversely, at any point "r" on the curve "c", let "t" be the tangent line at that point "r"; then there is a unique point "x" on the tangent "t" which forms with the pedal point "p" a line perpendicular to the tangent "t" (for the special case when the fixed point "p" lies on the tangent "t", the points "x" and "p" coincide) – the pedal curve is the set of such points "x", called the "foot" of the perpendicular to the tangent "t" from the fixed point "p", as the variable point "r" ranges over the curve "c".