How do I know what type of conics I have?

Cracking the Code: How to Spot Circles, Ellipses, Parabolas, and Hyperbolas Without Losing Your Mind

Conic sections. Sounds intimidating, right? But trust me, these shapes—circles, ellipses, parabolas, and hyperbolas—are way more interesting (and useful!) than the name suggests. They pop up all over the place, from the lenses in your glasses to the orbits of planets. The trick is learning to recognize them, especially from their equations. So, let’s break it down and make it easy.

The General Equation: Your Secret Decoder Ring

Think of this as the master key: