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In this paper we develop a systematic and self consistent procedure based ona set of compatibility conditions for identifying all maximal (eight parameter)and non-maximal (one and two parameter) symmetry groups associated with themixed quadratic-linear Li$\acute{e}$nard type equation, $\ddot {x} + f(x){\dot{x}}^{2} + g(x)\dot{x}+h(x)= 0$, where $f(x),\,g(x)$ and $h(x)$ are arbitraryfunctions of $x$. With the help of this procedure we show that a symmetryfunction $b(t)$ is zero for non-maximal cases whereas it is not so for themaximal case. On the basis of this result the symmetry analysis gets dividedinto two cases, $(i)$ the maximal symmetry group $(b\neq0)$ and $(ii)$non-maximal symmetry groups $(b=0)$. We then identify the most general form ofthe mixed-quadratic linear Li$\acute{e}$nard type equation in each of thesecases. In the case of eight parameter symmetry group, the identified generalequation becomes linearizable. We present a specific example of physicalinterest. In the case of non-maximal symmetry groups the identified equationsare all integrable. The integrability of all the equations is proved either byproviding the general solution or by constructing time independentHamiltonians. We also analyse the underlying equivalence transformations.

On the complete Lie point symmetries classification of the mixed  quadratic-linear Li$\acute{\textbf{e}}$nard type equation  $\ddot{x}+f(x)\dot{x}^2+g(x)\dot{x}+h(x)=0$