Hyperbolas and their equations.

1. 10.4 The Hyperbola
Objective: Find the equation, vertices, foci, and
asymptotes of hyperbolas.
Standard: Math Analysis 5.0

2. Definition of a Hyperbola:
The set of all points equidistant from ____________
________ where the __________ is constant.
Major axis is called the _____________ axis

3. Standard Equation:
Center:
Vertices:
Foci:
Asymptotes:

4. Why asymptotes?

5. Ex. 1) Graph and label the vertices, foci, and asymptotes.

6. Ex. 2) Find the standard form of the hyperbola with foci
at (0, 0) and (8, 0) and vertices at (3, 0) and (5, 0).

7. Ex. 3) Find the standard form of the hyperbola having
vertices at (2, 3) and (2, 9) and asymptotes of slope ±3/2.

8. Ex. 4) Find the slopes of the asymptotes of the
hyperbola given by the equation:

9. Ex. 5) Find the foci of the hyperbola with the equation:

11. Assignment:
#28 p. 760
#9, 10, 13-16, 22, 23,
27, 28, 45-55 (odd)