What is the difference between the shape of the graphs of $z=xy$ and $z=x^2-y^2$?
Are they different or just rotated? Kind of hard to confirm, because I know you can transform them.
But I don't know how or how to show that one is the transformation (rotation) of the other.
Let $u=x+y, v=x-y$. Then $z=uv$. So one graph is simply a rotation of the other, magnified by $2$ (to normalize $u$ and $v$).