In fact, this asymptote exists for any constant a where x3+y3=a3 :)
This is because, after putting y as the subject,
y
= (a3-x3)1/3
= [-x3(-a3/x3+1)]1/3
= -x(-a3/x3+1)1/3
And as x approaches +/- infinity, -a3/x3 approaches zero, thus -a3/x3+1 approaches 1. Therefore, the value of y approaches...