If an equation has a variable coefficient, will it also be considered as semilinear? (From chapter 1.3. Classification of equations, it looks like that coefficient as variable also results into a semilinear form.)

\begin{equation} Lu := a_{11}(x,y) u_{xx} + 2a_{12}(x,y) u_{xy} + a_{22}(x,y) u_{yy} = f(x,y,u,u_x,u_y)\end{equation}

Then questions like a) are semilinear homogeneous, which is a subgroup of nonlinear equation?