How to parameterize $x^{2n+1} + y^{2n+1} = 2 x^n y^n$ where parametrization is of form $$ x(t) = \rho(t) \cos^{\alpha} t $$ $$ y(t) = \rho(t) \sin^{\alpha} t $$ When I put that in the equation above, I got $$\rho(t) (\cos^{\alpha (2n+1)} t + \sin^{\alpha (2n+1)} t) = 2 \sin^{\alpha n} t \cos^{\alpha n} t$$ I have tried something like $\alpha = \frac{1}{2}$ and similar things but I have got nothing. Can someone please help?
2026-04-01 07:23:53.1775028233
Parameterize $x^{2n+1} + y^{2n+1} = 2 x^n y^n$
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