elliptical coordination

[fery]

I have a similarity variable which is an ellipse for my 2D pde, and I want to reduce the pde to 1d. the form of pde is div(fun/cir*n) which n is the normal vector on the similarity curve and cir is circumference of that. In polar coordination, it is trivial to reduce it to a 1d because circumference is a function of r, but I am kind of confused if the iso-potential curve be an ellipse.