In this chapter, we study a group of curves known as conic sections. One conic

section, the ellipse, has a special reflecting property responsible for “whispering

galleries.” In a whispering gallery, a person whispering at a certain point in the

room can be heard clearly at another point across the room.

The Old House Chamber of the U.S. Capitol, now called Statuary Hall, is a whis-

pering gallery. History has it that John Quincy Adams, whose desk was positioned at

exactly the right point beneath the ellipsoidal ceiling, often pretended to sleep there

as he listened to political opponents whispering strategies across the room. (Source:

Aikman, Lonnelle, We, the People, The Story of the United States Capitol.)

InSection 11.2,we investigate ellipses.

Nonlinear Functions, Conic

Sections, and Nonlinear Systems

11.1 Additional Graphs

of Functions

11.2 The Circle and

the Ellipse

11.3 The Hyperbola and

Functions Defined

by Radicals

11.4 Nonlinear Systems

of Equations

11.5 Second-Degree

Inequalities and

Systems of

Inequalities

635

11

CHAPTER