WHAT IS AN ELLIPSE?

DefinitionEquationGraph

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.

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.

EQUATIONAn 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

GRAPHS

Click here to see how the equation for an ellipse relates to its graph.

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

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.

WHY WOULD I WANT TO KNOW ABOUT ELLIPSES?

Whispering Galleries Planetary Orbits Haley’s Comet Lunar & Solar Eclipses Elliptical Galaxies

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