PrepZii

mixed

Standard Ellipse Geometry

The source gives the standard ellipse, eccentricity, directrices, foci, axes, vertices, and latus rectum.

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,\quad a>b

b^2=a^2(1-e^2)

e=\sqrt{1-\frac{b^2}{a^2}},\quad 0<e<1

x=\pm\frac{a}{e}

S=(\pm ae,0)

\text{major axis}=2a,\quad \text{minor axis}=2b

A'=(-a,0),\quad A=(a,0)

\ell=\frac{2b^2}{a}=2a(1-e^2)

$a$

parameter or semi-major axis depending on context

$b$

line coefficient or semi-minor axis depending on context

$e$

eccentricity