$X$ and $Y$ have bivariate normal distribution and have joint pdf
\begin{equation*}
f\left( x,y\right) =a\exp \left( \frac{-1}{2}\omega \right) ,\text{where }%
\omega =6x^{2}+12y^{2}-16xy-8x+24
\end{equation*}
then what are the means of $X$ and $Y$?
I have \begin{equation*} \frac{1}{\left( 1-\rho ^{2}\right) \sigma _{X}^{2}}=6,~\frac{1}{\left( 1-\rho ^{2}\right) \sigma _{Y}^{2}}=12~\text{and }\frac{-2\rho }{\left( 1-\rho ^{2}\right) \sigma _{X}\sigma _{Y}}=-16 \end{equation*} so i can find $\rho ,\sigma _{X}$ and $\sigma _{Y}$ using these equations. But how can i get $\mu _{X}$ and $\mu _{Y}$?
this question asked in an exam and requested to be replied in 2 minutes. Is there a shortcut for this?