1. Precalculus Section 6.4 Find and graph equations of hyperbolas Geometric definition of a hyperbola: A hyperbola is the set of all points in a plane such that the difference of the distances to two fixed points called foci is constant. Equation of a hyperbola whose center is at the origin: x 2 _ y 2 = 1 a 2 b 2 focal length relationship: c 2 = a 2 + b 2

2. example Graph the hyperbola, find the vertices and foci. x 2 _ y 2 = 1 36 9

3. example Graph and find vertices and foci. 16y 2 – 25x 2 = 400

4. The graph of an inverse variation is a rectangular hyperbola. Equation of a Rectangular Hyperbola xy = k Graph xy = 12 and xy = -12

5. example Write the equation of the hyperbola (center at origin) with a vertex at (6,0) and a focus at (10,0).

6. Equation of a hyperbola whose center is (h,k) ( x – h) 2 - (y – k) 2 = 1 a 2 b 2 (y – k) 2 - (x – h) 2 = 1 a 2 b 2

7. example Graph and find the vertices and foci. (y + 5) 2 - (x – 2) 2 = 1 9 16

8. example Graph x 2 – 9y 2 + 2x + 36y – 44 = 0

9. example Find the equation of the hyperbola whose center is (1,4) and has a vertex at (1,8) and a focus at (1,10).

10. assignment Page 235 Problems 2-8 even, 16,19,20,22,36,38,40,42,43,44