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Chapter 10

Any Way You Slice It: Conic Sections

In This Chapter

Writing equations of parabolas, circles, ellipses, and hyperbolas in standard form

Identifying centers, foci, and axes of conic sections

Sketching parabolas, circles, ellipses, and hyperbolas

Chapter 6 contains information on quadratic functions, which you graph as U-shaped curves called parabolas. Here, you see that not all parabolas represent functions. When a parabola opens to the left or right, you get more than one y-value for many x-values, and that just doesn’t work with functions. This chapter introduces parabolas and some other conic sections that don’t exactly fit the function mold. All parabolas are conic sections, but not all parabolas are functions — it depends on how they lie.

A conic section, or conic, is represented by a slice of a cone (or really, two cones stacked on top of each other, like an hourglass). How you slice the cone — at what angle and how big a chunk you take — determines what kind of conic section you produce. The four types of conic sections are the parabola, circle, ellipse, and hyperbola. Here’s how they compare:

• Parabola: You get this U-shaped curve when you take a slice through ...

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