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

Equations of Tangent of Hyperbola

\[Equation\]	\[Parametric\space Coordinates\]	\[Equation\space of\space tangent\]	\[Condition\space of \space Tangency\]
\[\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1\]	\[(asec\theta,btan\theta)\]	\[y=mx±\sqrt{am^2-b^2}\]	\[c=±\sqrt{am^2-b^2}\]
\[\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1\]	\[(bsec\theta,atan\theta)\]	\[y=mx±\sqrt{-bm^2+a^2}\]	\[c=±\sqrt{-bm^2+a^2}\]
\[{x^2}\space-{y^2}\space={a^2}\]	\[(asec\theta,atan\theta)\]	\[y=mx±\sqrt{am^2-a^2}\]	\[c=±\sqrt{am^2-a^2}\]

Equations of Normal of Hyperbola

\[Equation\]	\[Parametric\space Coordinates\]	\[Equation\space of\space Normal\]	\[Condition\space of \space Normality\]
\[\frac{x^2}{a^2}\space-\frac{y^2}{b^2}\space=1\]	\[(asec\theta,btan\theta)\]	\[\frac{ax}{sec\theta}+\frac{by}{tan\theta}=a^2+b^2\]	\[c=\frac{m(a^2+b^2)}{\sqrt{a^2-b^2m^2}}\]
\[\frac{y^2}{b^2}\space-\frac{x^2}{a^2}\space=1\]	\[(bsec\theta,atan\theta)\]	\[\frac{bx}{sec\theta}+\frac{ay}{tan\theta}=b^2+a^2\]	\[c=\frac{m(b^2-a^2)}{\sqrt{a^2m^2-b^2}}\]
\[{x^2}\space-{y^2}\space={a^2}\]	\[(asec\theta,atan\theta)\]	\[\frac{x}{sec\theta}+\frac{y}{tan\theta}=2a\]	\[c=\frac{2am}{\sqrt{1-m^2}}\]

Equations of Director Circle of Hyperbola

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