Find the length of a curve given by equations

Question

Find the length of a curve given by the equations $x^2+y^2+z^2=1$ and $(x^2+y^2)^2=x^2-y^2$

I tried with polar parametrization and with spherical parametrization but I can't solve the definite integral that I come up with.

Answer 1

$x(t) =r\cos t = \sqrt{\cos 2t}\cos t $

$y(t) =r\cos t = \sqrt{\cos 2t}\sin t $

$z(t) =\pm\sqrt{1-x^2 -y^2}=\pm\sqrt{1-\cos 2t}=\pm \sqrt{2}|\sin 2t|$