{(0, a)}

x(t) = 2 a t y(t) = a t^2

y = x^2/(4 a)

r(θ) = 4 a tan(θ) sec(θ)

(for a parabola opening upward with vertex at the origin and semilatus rectum 2a)

e = 1

y = -a

p = 2 a

L = 2 a