1. Definition Equation Graph
WHAT IS AN ELLIPSE?
Definition
Equation
Graph

2. What is an ellipse?
An ellipse is a conic section formed by the intersection of a plane and a cone.
Click here to see an applet that will allow you to display and animate the intersection of a plane and the surface of a cone.

3. DEFINITION
An ellipse is the set of all points in the plane such that the sum of the distances from two fixed points (called foci) is constant.
Note that this is clearly a geometrical definition and does not point out the relationship between an ellipse and its algebraic equation.

4. EQUATION
An ellipse with center at (x0 ,y0 ) can be defined algebraically in standard form by the equation:
It is important to remember:
a is the distance from the center to the end of major axis
b is the distance from the center to the end of major axis
c is the distance from the center to the focus
a2 = b2 + c2

5. GRAPHS
When graphing an ellipse it is useful to remember these facts:
center is (x0 ,y0 )
length of the major axis is 2a
length of the minor axis is 2b
distance between foci is 2a
Click here to see how the equation for an ellipse relates to its graph.

6. PRACTICE
Let’s try some practice problems and see what you have learned.
Click here for more practice problems.
Try these problems for more practice.

7. WHY WOULD I WANT TO KNOW ABOUT ELLIPSES?
Whispering Galleries
Planetary Orbits
Haley’s Comet
Lunar & Solar Eclipses
Elliptical Galaxies

8. THE END