Algebra II All-in-One For Dummies

Chapter 13

Slicing the Way You Like It: Conic Sections

IN THIS CHAPTER

Grasping the layout of a sliced cone

Investigating the standard equations and graphs of the four conic sections

Properly identifying conics with nonstandard equations

Conic is the name given to a special group of curves. What they have in common is how they’re constructed — points lying relative to an anchored point or points with respect to a line. But that sounds a bit stuffy, doesn’t it? Maybe it works better to think of conic sections in terms of how you can best describe the curves visually. Picture the Rainbow Bridge across the Niagara River. Imagine the earth’s path swinging around the sun. Reflect on the curved reflection plate in a car’s headlights. All these pictures circling your mind are related to curves called conics.

If you take a cone — imagine one of those yummy sugar cones that you put ice cream in — and slice it through in a particular fashion, the resulting edge you create will trace one of the four conic sections: a parabola, circle, ellipse, or hyperbola. (You can see a sketch of a cone in the following section. Well, actually, it’s two cones, lined up point-to-point.)

Each conic section ...