I'm doing an exercise and I have a doubt. It's the following:
A parameterization of the curve $C=(x,y,z)\in\mathbb{R}^3 : z=\sqrt{x^2+y^2},3y-5z+16=0\}$ could be:
a) $C:t \in [0,2\pi] \rightarrow C(t)=(4\cos t, 3+5\sin t, 5+3\sin t).$
b) $C:u \in [0,2] \rightarrow C(u)=(\frac{4}{5}\sqrt{25-(u+3)^2},u,\frac{3}{5}u+\frac{16}{5})$.
c) $C:u \in [-8,2] \rightarrow C(u)=(\frac{4}{5}\sqrt{25-(u+3)^2},u,\frac{3}{5}u+\frac{16}{5})$.
All options verify the relations in $C$, so I don't know which option could be. Is there someone who can help me?