Sections 8.2 and 8.3: Ellipses and Hyperbolas

To graph these conics.1.

To find the equation of a conic given certain info.2.

To solve apps.3.

Goals:

Definition: An ellipse is the set of all points in a plane the sum of whose distances from two distinct points (foci) is a constant.

Sections 8.2 and 8.3: Ellipses and HyperbolasTuesday, November 11, 201412:04 PM

Section 8.1 The Parabola as a Conic Section Page 1

Ex. Find the standard equation of the following ellipse and graph it. Also, find the foci.

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A circle is an ellipse where a = b1.

The eccentricity of an ellipse is e = c/a and is between 0 and 1. 2.

Note:

Ex. Comet Hale-Bopp orbits the sun in an elliptical orbit every 4200 years. At perihelion, the closest point to the sun, the comet is about 1 AU from the sun. At aphelion, the farthest point from the sun, the comet is 520 AU from the sun. Find an equation of the ellipse. What is the eccentricity of the orbit?

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Definition: A hyperbola is the set of all points in the plane the difference between whose distances from two fixed points (foci) is a constant.

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Ex. Graph the following hyperbola. Find the foci and the asymptotes.

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The eccentricity of a hyperbola is e = c/a. 1.

e>1.2.

As e becomes bigger the graph of the hyperbola widens

3.

Note:

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