For a curve given by a^(2/3)=abs(x)^(2/3)+abs(y)^(2/3). Find a differentiable parameterization, all singular points, and determine their type.
(Just common definations).
The Attempt at a Solution
Ok my thought was to find an arclength parameterization; however, the algebra is killing me. So far these are my steps, help would be greatly appreachited if you see a faster way.
abs(x)^2/3 + abs(y)^2/3=a^2/3 =>
And then I get stuck. I have tried other methods...but they aren't much nicer.
Any algebra hints tips would be great...(I can't believe I have forgotten how to do these).