\[Equation\]	\[Graph\]	\[Focus\]	\[Length\space of\space LR\]	\[Directrix\]	\[Length\space of\space Major\space Axis\]
\[\frac{x^2}{a^2}\space+\frac{y^2}{b^2}\space=1\] \[a>b\]		\[(±ae,0)\]	\[\frac{2b^2}{a}\]	\[x=±\frac{a}{e}\]	\[2a\]
\[\frac{x^2}{a^2}\space+\frac{y^2}{b^2}\space=1\] \[a < b\]		\[(0,±be)\]	\[\frac{2a^2}{b}\]	\[y=±\frac{b}{e}\]	\[2b\]

Equations of Tangent of Ellipse

\[Equation\]	\[Parametric\space Coordinates\]	\[Equation\space of\space tangent\]	\[Condition\space of \space Tangency\]
\[\frac{x^2}{a^2}\space+\frac{y^2}{b^2}\space=1\] \[a>b\]	\[(acos\theta,bsin\theta)\]	\[y=mx±\sqrt{am^2+b^2}\] \[\frac{xcos\theta}{a}+\frac{ysin\theta}{b}=1\]	\[c=±\sqrt{am^2+b^2}\]
\[\frac{x^2}{a^2}\space+\frac{y^2}{b^2}\space=1\] \[a < b\]	\[(bcos\theta,asin\theta)\]	\[y=mx±\sqrt{bm^2+a^2}\] \[\frac{xcos\theta}{b}+\frac{ysin\theta}{a}=1\]	\[c=±\sqrt{bm^2+a^2}\]

Equations of Normal of Ellipse

\[Equation\]	\[Parametric\space Coordinates\]	\[Equation\space of\space Normal\]	\[Condition\space of \space Normality\]
\[\frac{x^2}{a^2}\space+\frac{y^2}{b^2}\space=1\] \[a>b\]	\[(acos\theta,bsin\theta)\]	\[\frac{ax}{cos\theta}-\frac{by}{sin\theta}=a^2-b^2\]	\[c=±\frac{m(a^2-b^2)}{\sqrt{a^2+b^2m^2}}\]
\[\frac{x^2}{a^2}\space+\frac{y^2}{b^2}\space=1\] \[a < b\]	\[(bcos\theta,asin\theta)\]	\[\frac{bx}{cos\theta}-\frac{ay}{sin\theta}=b^2-a^2\]	\[c=±\frac{m(b^2-a^2)}{\sqrt{b^2+a^2m^2}}\]

Equations of Director circle of Ellipse

\[Equation\]	\[Equation\space of\space Director\space Circle\]
\[\frac{x^2}{a^2}\space+\frac{y^2}{b^2}\space=1\] \[a>b\]	\[x^2\,+\,y^2\space=\,a^2\,+\,b^2\]
\[\frac{x^2}{a^2}\space+\frac{y^2}{b^2}\space=1\] \[a < b\]	\[x^2\,+\,y^2\space=\,a^2\,+\,b^2\]