This is an rectangular hyperbola, so it is symmetric about x-axis , y-axis and origin.
Symmetric about y-axis if f(x,y) = f(-x,y)
3x^2-2y^2=3 <=> 3(-x)^2-2y^2=3
Symmetric about x-axis, if f(x,y) = f(x,-y)
3x^2-2y^2=3 <=> 3(x)^2-2(-y)^2=3
Symmetric about origin, if f(x,y) = f(-x,-y)
3x^2-2y^2=3 <=> 3(-x)^2-2(-y)^2=3