HyperbolaA hyperbola is a set of points P in a plane such that the difference between the distances from P to two fixed points F and F is a given constant.

Section 10-5 HyperbolasSunday, April 07, 2013

12:28 PM

Chapter 10 Page 1

To graph a hyperbola:1. use the standard form of the equation to find a and b. 2. Use a and b to find and graph the vertices and draw a central rectangle used to guide the graph. 3. Draw the asymptotes through the diagonals of the central rectangle4. Draw the branches of the hyperbola through the vertices so they approach the asymptotes.

Ex. 1 Graph

Chapter 10 Page 2

Find the Foci of hyperbolasThe coordinates of the foci are located on the transverse axis. If t.a. is horizontal: ( c, 0)If t.a. is vertical: (0, )

The distance between the foci, 2c is also the length of the diagonal of the central rectangle. So, you can use the pythagorean thm to find c.

Ex. 2 Find the foci of the graph. Draw the graph.

Chapter 10 Page 3

Ex. 3 Find the equation of a hyperbola that has one focus located at (4, 0) and one vertex located at (-2, 0). Assume that the center of the hyperbola is at the origin.

Chapter 10 Page 4