Why It Matters: Conic Sections*
What do the U.S Capitol Building in Washington, D.C., Grand Central Station in New York, and St. Paul’s Cathedral in London all have in common? Aside from being architectural marvels, each of these buildings contains a whispering gallery. A whispering gallery is most often an oblong enclosure beneath a dome or arch. These galleries get their name because a whisper in one part of the gallery can be heard clearly on the opposite side. Many movies and television shows have made use of whispering galleries in their plots as the conversations of the main characters are overhead. And tour guides at the U.S. Capitol recount a story in which John Quincy Adams used the whispering gallery to eavesdrop on conversations of other House members in the 1800s.
A whispering gallery can be produced through architecture alone, or it can be created using whispering dishes, which are large, flat dishes that reflect sound. The key is knowing exactly where to place the dishes. Suppose you are asked to create a whispering gallery in a room with an arch that has a width of 100 feet and a height of 40 feet. Where can you place the whispering dishes to create the gallery?
To answer this question, you’ll need to learn about conics. The arch represents one type of conic. At this end of this module, you can use what you’ve learned to create the whispering gallery.Learning Objectives
The Ellipse- Write equations of ellipses in standard form
- Graph ellipses centered at the origin
- Graph ellipses not centered at the origin
- Solve applied problems involving ellipses
- Locate a hyperbola’s vertices and foci
- Write equations of hyperbolas in standard form
- Graph hyperbolas centered at the origin
- Graph hyperbolas not centered at the origin
- Solve applied problems involving hyperbolas
- Graph parabolas with vertices at the origin
- Write equations of parabolas in standard form
- Graph parabolas with vertices not at the origin
- Solve applied problems involving parabolas
