I have done questions like these before, except I've never seen one with three variables inside the function, asking for only two independent variables.
What is the significance of variable(a) in this equation? I have no idea what to do here, all I've done so far is found the partial derivative of z with respect to x, with respect to y, and with respect to a.
Because it says $z(x,y)$ we can infer that $a$ is a constant, not a variable so you don't have to take partial derivatives with respect to $a$ just $x$ and $y$.