How do you find conic sections?

Decoding the Curves: A Friendly Guide to Conic Sections

Ever wondered about those cool shapes – circles, ellipses, parabolas, and hyperbolas – that pop up all over the place, from the curve of a satellite dish to the path of a planet? These are conic sections, and they’re not as intimidating as they might sound! Basically, they’re what you get when you slice a cone with a plane, and figuring out which one you’re looking at is a neat trick.

So, how do you actually spot them? Well, it all starts with a general equation – think of it as the master key that unlocks all conic sections: