equilateral hyperbola | right hyperbola

x(t) = a sec(t) y(t) = a tan(t)

x^2 - y^2 = a^2

r(θ) = a sqrt(sec(2 θ))

(for a hyperbola with center at the origin, semimajor axis a parallel to the x-axis, and semiminor axis a parallel to the y-axis)

algebraic | conic | parametric | quadratic

d = 2

e = sqrt(2)

{(-sqrt(2) a, 0), (sqrt(2) a, 0)}

p = a/sqrt(2)

x = -a/sqrt(2) ∨ x = a/sqrt(2)