Alinhamento central vertical do texto na célula da tabela

Question

Estou tentando criar a seguinte tabela

Mas o problema é que os grandes colchetes na terceira coluna estão nas linhas horizontais. Existe alguma maneira de centralizar os colchetes verticalmente de maneira fácil?

\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

Sugiro usar {NiceTabular}o nicematrixque fornece parâmetros cell-space-bottom-limite cell-space-top-limitinspirado nos comprimentos \cellspacebottomlimite \cellspacetoplimitna embalagem cellspace.

{NiceTabular}foi projetado para fornecer melhores resultados do que o padrão colortblnos visualizadores de PDF quando as regras são usadas em conjunto com painéis coloridos. No entanto, você precisa de várias compilações.

\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

Com o uso dos nccmathpacotes cellspace, hhlinee e arraypara tabela:

\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}

Termo aditivo: Versão onde as equações nas células são alinhadas com sinal de igual e pontos entre vírgulas:

\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}