1. What is it?

2. Definition: A hyperbola is the set of points P(x,y) in a plane such that the absolute value of the difference between the distances from P to two fixed points in the plane, F 1 and F 2, called the foci, is a constant. 9.5 Hyperbolas

3. Transverse axis Conjugate Axis Vertices Co-vertices Center Foci Asymptotes (2a) length of V to V (2b) length of CV to CV Endpoints of TA Endpoints of CA Intersection of the 2 axes Lie on inside of hyperbola Horizontal Vertical (When centered at the origin) 9.5 Hyperbolas

4. Notes:  a 2 is always the denominator of the ________ term when the equation is written in standard form.  _________ axis can be longer or ____________  The length of the transverse axis is _________ he length of the conjugate axis is _________  a 2 + b 2 = c 2 9.5 Hyperbolas 1st Eithershorter 2a 2b

5. a 2 always comes 1 st !

6. What is the equation?

12. How would you graph each?

13. What is the equation?

19. Place the equation with the graph.

20. Example 1: Write the standard equation of the hyperbola with vertices (-5,0) and (5,0) and co-vertices (0, -2) and (0, 2). Sketch the graph.

21. Example 2: Write the standard equation of the hyperbola with V (0,-3) (0, 3) and CV(-6, 0) (6, 0)

22. Example 3: Find the equation of the asymptotes and the coordinates of the vertices for the graph of Then graph the hyperbola.

23. Example 4: Graph. Identify the center, vertices, foci, and asymptotes of the hyperbola.

24. Example 5: Graph 25y 2 – 4x 2 = 100. Identify the center, vertices, foci, and asymptotes of the hyperbola.

25. Assignment: