Do not adjust your TV set. Those are not a pair of parabolas frolicking in that cone. No, they are actually a single conic section, and our last one, the hyperbola.
We wouldn't blame you for mistaking it for some parabolas, though. Hyperbolas get that a lot. Each half has a directrix outside of the curve, a vertex, and a focus that is inside the curve, just like a parabola. Hyperbolas also have an axis of symmetry, the transverse axis, that goes through all of the vertices, foci, and the center. Fancy shmancy. The big difference from parabolas is that both these curves are juggled at the same time.
Actually, the big HUGE difference is that hyperbolas have two asymptotes. They crisscross through the hyperbola's center, and the hyperbola's arms approach but never touch them as they all wander off into infinity.
As you probably could guess, hyperbolas can be horizontal or vertical. The transverse axis has the same orientation as the hyperbola, horizontal or vertical. Which way the graph opens all depends on whether x or y come first in the equation. But that's getting ahead of ourselves, and being both ahead and behind ourselves gets confusing quickly.