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Writing Equations of Ellipses

The Ellipse

Learning Objectives

In this section, you will:

  • 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.


Figure 1 The National Statuary Hall in Washington, D.C.

Can you imagine standing at one end of a large room and still being able to hear a whisper from a person standing at the other end? The National Statuary Hall in Washington, D.C., shown in Figure 1, is such a room. It is an oval-shaped room called a whispering chamber because the shape makes it possible for sound to travel along the walls. In this section, we will investigate the shape of this room and its real-world applications, including how far apart two people in Statuary Hall can stand and still hear each other whisper.

Source: Rice University, https://openstax.org/books/college-algebra/pages/8-1-the-ellipse
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