I have this exercise: The question as it is written in the book. $z = x^{2}$ and $z = 4y^{2}$ intersect in two curves, one of which goes through the point $(2, -1, 4)$. Parameterize that curve.
My attempt: I parameterized using t=y. Got this result:$ x= \pm 2t$, $y =t$, $z= 4t^{2}$ Now, I know that x cannot have both a minus and a plus sign since they denote different curves. However I don't know how to think when deciding on the sign of $x$. I chose $x = -2t$ in the end because "it felt right" and it happened to be correct. But, I don't understand how I should think when deciding on this point.