Consider the parametric curve $$A(a) = \langle -\sqrt{2} \sin(a),\cos(a),\sin(a) \rangle$$ for $0 \leq a \leq 2 \pi.$ We may obtain a unit parametrization of $A$ by
$$B(a) = \frac{A(a)}{||A(a)||} = \frac{A(a)}{\sqrt{1+2 \sin^{2}(a)}}$$ for $0 \leq a \leq 2 \pi.$ I guess $B$ is a "slanted circle." Can I get the equation of $B?$