# Vertical center alignment of text in cell of table

With use of the nccmath, cellspace, and hhline packages and array for table:


\documentclass{article}
\usepackage{nccmath}
\usepackage[table]{xcolor}
\usepackage{cellspace, hhline}
\setlength\cellspacetoplimit{5pt}
\setlength\cellspacebottomlimit{5pt}

\begin{document}
$\begin{array}{ |c | c | >{}Sc<{}|} \hhline{---} \rowcolor{blue!50} \text{\textcolor{white}{Parabola}} & \text{\textcolor{white}{Equation of Tangent}} & \text{\textcolor{white}{Point of Contact}} \\ \hhline{---} y^2=4ax & y=mx+\frac{a}{m} & \Bigl(\mfrac{a}{m^2},\mfrac{2a}{m}\Bigr) \\ \hhline{---} y^2=-4ax & y=mx-\dfrac{a}{m} & \Bigl(-\mfrac{a}{m^2},\mfrac{2a}{m}\Bigr) \\ \hhline{---} x^2=4ay & y=mx-am^2 & \bigl(2am,am^2\bigr) \\ \hhline{---} {x^2=-4ay} & y=mx+am^2 & \bigl(-2am,-am^2\bigr) \\ \hhline{---} \end{array}$
\end{document}


Addendum: Version where equation in cells are aligned at equal sign and points at commas:

\documentclass{article}
\usepackage{nccmath}
\usepackage[table]{xcolor}
\usepackage{cellspace, hhline}
\setlength\cellspacetoplimit{5pt}
\setlength\cellspacebottomlimit{5pt}
\usepackage{xparse}
\NewExpandableDocumentCommand\mcw{O{>{\color{white}}Sc|}m}
{\multicolumn{2}{#1}{#2}}
\usepackage[skip=1ex]{caption}

\begin{document}
$\setlength\arrayrulewidth{0.5pt} \setlength\arraycolsep{12pt} \begin{array}{ |r@{\,}l | >{\qquad}r@{\,}l | r@{,\,}>{}Sl<{}|} \hhline{*{6}{-}} \rowcolor{blue!50} \mcw[|>{\color{white}}Sc|]{Parabola} & \mcw{Equation of Tangent} & \mcw{Point of Contact} \\ \hhline{*{6}{-}} y^2 & = 4ax & y & =mx+\frac{a}{m} & \Bigl(\mfrac{a}{m^2} & \mfrac{2a}{m}\Bigr) \\ \hhline{*{6}{-}} y^2 & = -4ax & y & = mx-\dfrac{a}{m} & \Bigl(-\mfrac{a}{m^2} & \mfrac{2a}{m}\Bigr) \\ \hhline{*{6}{-}} x^2 & = 4ay & y & = mx-am^2 & \bigl(2am & am^2\bigr) \\ \hhline{*{6}{-}} x^2 & = -4ay & y & = mx+am^2 & \bigl(-2am & -am^2\bigr) \\ \hhline{*{6}{-}} \end{array}$
\end{document}


I suggest to use {NiceTabular} of nicematrix which provides parameters cell-space-bottom-limit and cell-space-top-limit inspired by the lengths \cellspacebottomlimit and \cellspacetoplimit of the package cellspace.

{NiceTabular} is designed to give better results than standard colortbl in the PDF viewers when rules are used in conjonction with colored panels. However, you need several compilations.

\documentclass{article}

\usepackage{nicematrix}

\begin{document}
\begin{center}
\everymath{\displaystyle}
\NiceMatrixOptions{cell-space-top-limit=2pt,cell-space-bottom-limit=2pt}
\begin{NiceTabular}{ccc}[hvlines,colortbl-like]
\rowcolor{blue!50} \textcolor{white}{Parabola} & \textcolor{white}{Equation of Tangent} & \textcolor{white}{Point of Contact} \\
$y^2=4ax$& $y=mx+\frac{a}{m}$& $\biggl(\frac{a}{m^2},\frac{2a}{m}\biggr)$  \\
$y^2=-4ax$ & $y=mx-\frac{a}{m}$ & $\biggl(-\frac{a}{m^2},\frac{2a}{m}\biggr)$  \\
$x^2=4ay$ & $y=mx-am^2$& $\bigl(2am,am^2\bigr)$  \\
$x^2=-4ay$ & $y=mx+am^2$& $\bigl(-2am,-am^2\bigr)$  \\
\end{NiceTabular}
\end{center}
\end{document}