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

e=\frac{c}{a} \lt 1

x= \pm \frac{a}{e} = \pm \frac{a^2}{c}

\begin{cases} x=a.cost \\ y=b.sint \end{cases} \qquad 0 \le t \le 2\pi

Ax^2+Bxy+Cy^2+Dx+Ey+F=0 \qquad B^2-4AC \lt 0

Ax^2+Cy^2+Dx+Ey+F=0 \qquad AC \gt 0

L=4aE(e) \end{align} \begin{align} \text{where the function $E$ is the complete elliptic integral of the second kind}

& L=\pi(1.5(a+b)-\sqrt[]{ab}) \\ & L=\pi\sqrt[]{2(a^2+b^2)}

r_{1}+r_{2}=2a \end{align} \begin{align} \text{where $r_{1}$, $r_{2}$ are distances from any point $P(x,y)$ on the ellipse to the two foci.}

a^2=b^2+c^2

S=\pi ab