  Given $\Omega(\subseteq\;R^{1+m})$, a smooth bounded domain and a nonnegative
measurable function $f$ defined on $\Omega$ with suitable summability. In this
paper, we will study the existence and regularity of solutions to the
quasilinear degenerate elliptic equation with a singular nonlinearity given by:
\begin{align} -\Delta_\lambda u&=\frac{f}{u^{\nu}} \text{ in }\Omega\nonumber
&u>0 \text{ in } \Omega\nonumber &u=0 \text{ on } \partial\Omega\nonumber
\end{align} where the operator $\Delta_\lambda$ is given by
$$\Delta_\lambda{u}=u_{xx}+|x|^{2\lambda}\Delta_y{u};\,(x,y)\in \;R\times\;R^m
$$ is known as the Grushin operator.
