- #1

^_^physicist

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## Homework Statement

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.

## Homework Equations

(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 =>

1+abs(y^(2/3)/x^(2/3))=(a^(2/3))/(abs(x^(2/3))=>

[abs(y^(2/3)/x^(2/3))+1]^(3/2)=abs(a/x)

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).