\[Equation\] \[Graph\] \[Focus\] \[Length\space of\space LR\] \[Equation\space of\space Directrix\] \[Equation\space of\space Axis\]
\[y^2=4ax\] \[(a,0)\] \[4a\] \[x=-a\] \[y=0\]
\[y^2=-4ax\] \[(-a,0)\] \[4a\] \[x=a\] \[y=0\]
\[x^2=4ay\] \[(0,a)\] \[4a\] \[y=-a\] \[x=0\]
\[x^2=-4ay\] \[(0,-a)\] \[4a\] \[y=a\] \[x=0\]

Equations of Tangent of all Parabolas in slope form

\[Equations\space of\]
\[Parabola\]
\[Point\space of\space contact\space in\]
\[\space terms\space of\space slope(m)\]
\[Equation\space of\space tangent\space in\]
\[\space terms\space of\space slope(m)\]
\[Condition\space of\space Tangency\]

\[y^2=4ax\] \[(\frac{a}{m^2},\frac{2a}{m})\] \[y=mx+\frac{a}{m}\] \[c=\frac{a}{m}\]
\[y^2=-4ax\] \[(-\frac{a}{m^2},-\frac{2a}{m})\] \[y=mx-\frac{a}{m}\] \[c=-\frac{a}{m}\]
\[x^2=4ay\] \[(2am,am^2)\] \[y=mx-am^2\] \[c=-am^2\]
\[x^2=-4ay\] \[(-2am,am^2)\] \[y=mx+am^2\] \[c=am^2\]

Equations of Normal of all Parabolas in slope form

\[Equations\space of\]
\[Parabola\]
\[Point\space of\space contact\space in\]
\[\space terms\space of\space slope(m)\]
\[Equation\space of\space normal\space in\]
\[\space terms\space of\space slope(m)\]
\[Condition\space of\space Normality\]

\[y^2=4ax\] \[(am^2,-2am)\] \[y=mx-2am-am^3\] \[c=-2am-am^3\]
\[y^2=-4ax\] \[(am^2,2am)\] \[y=mx+2am+am^3\] \[c=2am+am^3\]
\[x^2=4ay\] \[(-\frac{2a}{m},\frac{a}{m^2})\] \[y=mx+2a+\frac{a}{m^2}\] \[c=2a+\frac{a}{m^2}\]
\[x^2=-4ay\] \[(\frac{2a}{m},-\frac{a}{m^2})\] \[y=mx-2a-\frac{a}{m^2}\] \[c=-2a-\frac{a}{m^2}\]

Director Circle of all Parabolas

\[Equations\space of\space Parabola\] \[Equation\space of\space Director\space Circle\]
\[y^2=4ax\] \[x\,+a\space=\,0\]
\[y^2=-4ax\] \[x\,-a\space=\,0\]
\[x^2=4ay\] \[y\,+a\space=\,0\]
\[x^2=-4ay\] \[y\,-a\space=\,0\]