1. Hyperbola
Objective:
Be able to get the equation of a hyperbola from given information or the graph
Be able to find the key features of and graph a hyperbola
Thinking Skill: Explicitly assess information
and draw conclusions
Warm Up:
Try to recall the standard form of a hyperbola’s equation
And use it to find the equation of a hyperbola with a center
of (1, -1), a vertex of (3, -1) and a foci at (4, -1).

2. Hyperbola
Definition: A hyperbola is the set of all points (x, y) where the difference of the distances from two fixed points (foci) is constant
Equations
Horizontal – Vertical
Asymptotes Asymptotes
Where the center is (h, k), and a2 + b2 = c2

3. Examples
Find the center, vertices, foci and asymptotes of then graph.

4. Examples
Find the center, vertices, foci and asymptotes then graph

5. Examples
Find the equation of the hyperbola with foci (-1, 2) and (5, 2) and vertices (0, 2) and (4, 2).

6. Examples
Find the equation of the hyperbola with foci (10, 0) and (-10, 0) and asymptotes of y = ¾x and y = -¾x

7. Two microphones, 1 mile apart, record an explosion
Two microphones, 1 mile apart, record an explosion. Microphone A receives the sound 2 seconds before microphone B. Find an equation representing where the explosion occurred. Note: 5280ft = 1mi & sound travels 1100ft/sec

8. Closing Problem
Find the standard form equation of the hyperbola with vertices of (-1, 3) & (-1, 9) and a focus of (-1, -1).