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Hyperbola

Example plots

Equations

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

x^2/a^2 - y^2/b^2 = 1

r(θ) = (a b)/sqrt(b^2 cos^2(θ) - a^2 sin^2(θ))

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

Properties

algebraic | conic | parametric | quadratic

Basic properties

d = 2

Conic properties

e = sqrt(b^2/a^2 + 1)

p = b^2/sqrt(a^2 + b^2)

L = b^2/a

${(-sqrt(a^2 + b^2), 0), (sqrt(a^2 + b^2), 0)}$

y = -(b x)/a ∨ y = (b x)/a

x = -a^2/sqrt(a^2 + b^2) ∨ x = a^2/sqrt(a^2 + b^2)