Beautiful Equation

$\large 8\dfrac{\partial^2 z}{\partial x^2} - 2\dfrac{\partial^2 z}{\partial x \partial y} - 3\dfrac{\partial^2 z}{\partial y^2} = 0$

Consider the Second order PDE above, then which of the following is True for arbitrary differentiable functions $f$ and $g$ ?

1: the equation is Elliptic and the general solution is $z = f\left(y - \dfrac{x}{2}\right) + g\left(y + \dfrac{3x}{4}\right)$ .

2: the equation is Hyperbolic and the general solution is $z = f\left(y - \dfrac{x}{2}\right) + g\left(y + \dfrac{3x}{4}\right)$ .

3: the equation is Parabolic and the general solution is $z = f\left(y + \dfrac{x}{2}\right) + g\left(y - \dfrac{3x}{4}\right)$ .

4: the equation is Elliptic and the general solution is $z = f\left(y + \dfrac{x}{2}\right) + g\left(y - \dfrac{3x}{4}\right)$ .