How to show that the bipolar co-ordinates are othogonal
where $x=\dfrac{\sin hv}{\cos hv-\cos u},y=\dfrac{\sin u}{\cos hv-\cos u},z=z$
where $u\in [0,2\pi]$ and $y,z\in (-\infty,\infty)$.
How to show a system is orthogonal?
Do I need to compute the angle between them?If yes how to do it?
Hint.
Given $x(u,v), y(u,v)$ find
$t_x = (x_u,x_v), \, t_y = (y_u, y_v)$
and then verify that
$t_x\cdot t_y = 0$