Chapter 22
CONIC SECTIONS
The conic sections are a collection of equations that contain x and y raised
to the second power. Among them, only parabolas contain a single vari-
able that is squared, whereas circles, ellipses, and hyperbolas contain two
squared variables. In this chapter, the standard form and defining geomet-
ric characteristics of each conic section are explored.
This chapter starts out with a discussion of parabolas, which are the
graphs of quadratic equations that contain x and y. Your goal will be to
write parabolas in standard form and identity some of their parts, such as
the vertex, the focus, and the directrix.
Warning! To put conic sections in standard form, you need to be able to
complete the square. If you don’t know how, review Problems 14.12–14.19.
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