The document discusses ellipses and provides examples of their key properties and equations. It defines an ellipse as the set of all points where the sum of the distances from two fixed points (foci) is constant. It notes that Statuary Hall in the US Capitol building has an elliptical ceiling where one can hear conversations near the focal points. Examples are given of writing equations of ellipses given information about their axes, centers, and endpoints. Readers are asked to find properties of ellipses from equations and graph them.

2. Ellipse
© Jill Britton, September 25, 2003
•Statuary Hall in the U.S. Capital building is elliptic. It was in this room that John Quincy
Adams, while a member of the House of Representatives, discovered this acoustical
phenomenon. He situated his desk at a focal point of the elliptical ceiling, easily
eavesdropping on the private conversations of other House members located near the
other focal point.

3. •An ellipse is the set of all points in a plane such that the sum
of the distances from two fixed points is constant.
Major Axis = 2a
Minor Axis = 2b
Major Axis = 2a
(x-h)2 + (y-k)2 = 1 (y-k)2 + (x-h)2 = 1
a2 b2 a2 b2
Center = (h, k)
*The larger denominator indicates the Major Axis*

4. Writing an equation based on a graph
•Write an equation for the
ellipse pictured.

5. Writing equations given information
1) Major axis 8 units long and parallel to x-axis, minor axis 2 units
long and parallel to y-axis, center at (-2, 5).
2) Endpoints of the major axis (-7, 2) and (5, 2), endpoints of minor
axis (-1, 0) and (-1, 4)

6. Graphing Ellipses
•Find the coordinates of the center and the lengths of the major
and minor axes for the ellipse within the given equation. Then
graph the ellipse.
1) 2)

7. HW: Worksheet