Simplify & Polar Plot ?

We already had this in another thread of yours:

So get rid of the unnecessary absolute value in r1 and tell Mathcad that k is a real, too

You now get the solution not only for k=1 but for any (real) k:

Next time you have troubles with the absolute function with real(!) arguments, you could instead use

Using this replacement (for reals only! Not for non-reals and also not for vectors!) you can even use the unnecessary absolute value in r1