Variables

a
→
Semimajor axis
b
→
Semiminor axis
F1(-c,0)
→
Left focus
F2(c,0)
→
Right focus
P
→
Perimeter
A
→
Area
e
→
Eccentricity
1.
Equation of an Ellipse
$\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$
Ellipse
Equation
2.
$r_1 + r_2 = 2a$
Ellipse
Foci
3.
$a^2 = b^2 + c^2$
Ellipse
4.
Eccentricity
$e=\dfrac{c}{a}$
Ellipse
5.
Equation of Directrices - version 1
$x = \pm \dfrac{a}{e}$
Ellipse
6.
Equation of Directrices - version 2
$x = \pm \dfrac{a^2}{c}$
Ellipse
7.
Parametric form of a ellipse
$\begin{array}{ll} x =& a \cos t \\ y =& b \sin t \end{array} 0\le t \le 2 \pi$
Ellipse
8.
General form of a Ellipse
$Ax^2+Bxy+Cy^2+DX+Ey+F=0$, where $B^2-4AC < 0$
Ellipse
9.
Circumference of an elliplse
$P = 4aE(e)$
Ellipse
10.
Circumference of an elliplse - approximation 1
$P=\pi\left(\dfrac{3}{2}(a+b)-\sqrt{ab}\right)$
Ellipse
11.
Circumference of an elliplse - approximation 2
$P=\pi \sqrt{2\left(a^2+b^2\right)}$
Ellipse
12.
Ellipse area
$A = \pi a b$
Ellipse

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