# Eliminating variables

zpconn

## Homework Statement

I have the equations x = a * sinh(u) / (cos(v) + cosh(u)) and y = a * sin(v) / (cos(v) + cosh(u)). I believe that if a value of u is fixed, then the locus of (x,y) satisfying these equations is a circle depending on v. Similarly, I believe that if a value of v is fixed, then the locus of (x,y) satisfying these equations is a circle depending on u.

I would like to verify this.

## The Attempt at a Solution

It seems the easiest way is to find the equations of the circles by somehow eliminating either u or v, but I can't figure out how. I've employed various identities, such as cosh^2 - sinh^2 = 1, but I can never fully eliminate one variable.