Hyperbola formulas

→

Transverse axis

→

Conjugate axis

F1(-c,0)

→

Left focus

F2(c,0)

→

Right focus

s, t

→

Asymptotes

→

Eccentricity

Equation of a Hyperbola

$\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$

$|r_1-r_2| = 2a$

Equations od Asymptotes

$y=\pm\dfrac{b}{a}x$

$c^2=a^2+b^2$

Hyperbola eccentricity

$e=\dfrac{c}{a}$

Equations of directrices

$x=\pm\dfrac{a}{e}$

Parametric equation of the right branch

$\begin{array}{ll} x = a \cosh t \\[1 em] y=b \sinh t \end{array} 0\le t \le 2\pi$

General form of a hyperbola

$Ax^2+Bxy+Cy^2+Dx+Ey+F=0$, where $B^2-4AC > 0 $