#hyperbole hyperbolas

We are currently studying conic sections in the pre-calc class that I teach. This includes ellipses, parabolas, and hyperbolas. Occasionally, one of my students calls hyperbolas (conic section) “hyperboles” (exaggerated statement; not meant to be taken literally). I’ve personally always thought that hyperbolas and hyperboles go hand in hand, because hyperbolas are so. freaking. dramatic.

See, here’s an ellipse:

Here’s a parabola:  

Nice, friendly conic sections. You’d be happy if these fellas came over to hang out after school, right? 

Now, here’s a hyperbola: 

Like, what even is this guy’s deal? See, hyperbolas not only go in TWO directions, they also have their entourage of asymptotes following along (the blue lines). They are literally the most dramatic conic sections. Just like...what you tryin’ to prove there, my little friend?

Anyhow, all this preamble to say that in the middle of class today, I just straight up looked my junior-high girls in the eye and said:

“Hyperbolas are SO extra”