Vertical center alignment of text in cell of table

Question

I am trying to create following table

But the problem is that the big round brackets in third column are sitting on the horizontal lines. Is there some way to center align the brackets vertically in an easy manner?

\begin{tabular}{ |c | c | c|}

\hline
\rowcolor{myblue} \textcolor{white}{Parabola} & \textcolor{white}{Equation of Tangent} & \textcolor{white}{Point of Contact} \\ 

 \rule{0pt}{25pt}\bm{$y^2=4ax$} & \bm{$\displaystyle y=mx+\frac{a}{m}$} & \bm{$\displaystyle \bigg(\frac{a}{m^2},\frac{2a}{m}\bigg)$}   \\ \hline  
 
\rule{0pt}{25pt}\bm{$y^2=-4ax$} & \bm{$\displaystyle y=mx-\frac{a}{m}$} & \bm{$\displaystyle  \bigg(-\frac{a}{m^2},\frac{2a}{m}\bigg)$}   \\  \hline
  
\rule{0pt}{20pt}\bm{$x^2=4ay$} & \bm{$\displaystyle y=mx-am^2$} & \bm{$\displaystyle \big(2am,am^2\big)$}   \\ \hline  
 
\rule{0pt}{20pt}\bm{$x^2=-4ay$} & \bm{$\displaystyle y=mx+am^2$} & \bm{$\displaystyle \big(-2am,-am^2\big)$}   \\   \hline 

\end{tabular}

Answer 1

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}

Answer 2

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}