circle pedal curve

x(t) = cos(t) (a - y_0 sin(t)) + x_0 sin^2(t) y(t) = 1/2 (2 a sin(t) - x_0 sin(2 t) + y_0 cos(2 t) + y_0)

(x^2 - x_0 x + y (y - y_0))^2 = a^2 ((x - x_0)^2 + (y - y_0)^2)

(for a circle with center at the origin, radius a, and pedal point (x_0, y_0))

algebraic | closed | loopy | pedal | quartic

A^* = 1/2 π (2 a^2 + x_0^2 + y_0^2)

s = 4 sqrt(a^2 - 2 a sqrt(x_0^2 + y_0^2) + x_0^2 + y_0^2) E(-(4 a sqrt(x_0^2 + y_0^2))/(a^2 - 2 sqrt(x_0^2 + y_0^2) a + x_0^2 + y_0^2))

d = 4