Conic Sections Introduction
At a celebration of one of Shmoop's favorite subjects (let’s face it; they’re all our favorite and we just like a celebration), one of our monkey interns got a hold of the cake knife and went all ninja on the party hats, slicing them at various angles. Everyone was upset until someone pointed out that the monkey had just formed four conic sections out of the party hats.
Party hats are shaped like cones, just like ice cream cones. Picture these whenever we’re talking about conic sections. Why? Because we really like parties and ice cream. Also because the conic sections are formed by drawing a line straight through some cones.
A circle is revealed if we slice straight across a cone. If the slice is taken parallel to one of the sloping sides of the cone, then we get a parabola. We would remember this curve from algebra, but we've blocked that out of our memory. It was a hard time for us.
Any cut made with an angle less than the parabola, but more than the circle, will produce an elongated shape called an ellipse. Finally, some slices like the cone so much that they cut it twice, resulting in a hyperbola. They look like two separate curves, but they belong to the same shape.
Everyone immediately recognized the brilliant improvement the monkey had made to the party hats in making them represent one of the greatest geometric marvels in mathematics, conic sections. We all agreed that was one smart monkey.