1. More Practice with Hyperbolas
…in Sec. 8.3b

2. Nifty Practice Problems
Write an equation for the given hyperbola.
The hyperbola opens up-down:
(2, –2)
Plug in the point (2, –2):
Equation:

3. Definition: Eccentricity of a Hyperbola
The eccentricity of a hyperbola is
where a is the semitransverse axis, b is the
semiconjugate axis, and c is the distance
from the center to either focus.
Eccentricity of a hyperbola is always greater than 1!!!

4. Nifty Practice Problems
Find an equation in standard form for the hyperbola with
center at (0, 0), a = 4, e = 3/2, and a vertical focal axis.
Start with a diagram?
What’s the general equation?
How about h and k?
Now, how do we find a and b?

5. Nifty Practice Problems
Find an equation in standard form for the hyperbola with
center at (0, 0), a = 4, e = 3/2, and a vertical focal axis.
The specific equation:

6. Nifty Practice Problems
Find an equation in standard form for the hyperbola with
center at (1, –4), c = 6, e = 2, and a horizontal focal axis.

7. Nifty Practice Problems
Graph the given hyperbola, and find its vertices, foci, and
eccentricity.
Where’s the graph?
Vertices:
Foci:
Eccentricity:

8. Nifty Practice Problems
Graph the given hyperbola, and find its vertices, foci, and
eccentricity.

9. Nifty Practice Problems
Graph the given hyperbola, and find its vertices, foci, and
eccentricity.
Where’s the graph?
Vertices:
Foci:
Eccentricity: