Section 7.4 The Hyperbola Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

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Section 7.4 The Hyperbola Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Distance from center to focus is c = 3 Finding an equation of the hyperbola with center at the origin, one focus at (3, 0), and one vertex at ( 2, 0). Graph the equation. Distance from center to focus is c = 3 Distance from center to vertex is a = 2. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Find an equation of the hyperbola having one vertex at (0, 2) and foci at (0, 3) and (0, 3). Graph the equation. Looking at the points given we see that the center is at (0,0) and the transverse axis is along the y-axis. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Since the y2 term is positive, the transverse axis is along the y-axis. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Asymptotes: Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Distance from center to a focus is c = 3 Find an equation for the hyperbola with center at (1,  2), one focus at (4, 2), and one vertex at (3, 2). Graph the equation by hand. Center, focus and vertex are on y = 2 so tranvserse axis is parallel to x-axis. Distance from center to a focus is c = 3 Distance from center to a vertex is a = 2 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.