Writing Equations of Ellipses

First, we will focus on ellipses and the components that make up the equation for an ellipse. You will learn how to write the equation of an ellipse given different components of the ellipse.

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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