The fact that the exponents on x and y are even so that and would lead me to say that the graph is symmetric about the axes: the point "symmetric" to (x, y) about the y-axis is (-x, y) and about the x-axis is (x, -y). The fact that the formula is "symmetric" with respect to x and y: replacing x with y and y with x changes to which is the same equation, tells me that it is symmetric about the lines y= x and y= -x.