Hyperbolas in Standard Form

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Show your work for each problem.

1.
Which equation represents a hyperbola with a horizontal transverse axis?
1. a)
2. b)
3. c)
4. d)
2.
For the hyperbola , what is the value of ?
1. a)
2. b)
3. c)
4. d)
3.
What is the center of the hyperbola ? Enter as
4.
For a hyperbola with and , what is ?
5.
What are the vertices of the hyperbola ?
1. a) and
2. b) and
3. c) and
4. d) and
6.
What is the slope of the asymptotes for ? Enter as a fraction.
7.
What are the foci of ?
1. a) and
2. b) and
3. c) and
4. d) and
8.
Find the center, vertices, and foci of
9.
Write the standard form equation for a hyperbola with center , vertex at , and focus at . Enter as y^2/a - x^2/b = 1
10.
What is the equation of the asymptotes for ?
1. a)
2. b)
3. c)
4. d)
11.
Convert to standard form.
12.
A hyperbola has foci at and , and the difference of distances from any point on the hyperbola to the foci is 8. What is ?
13.
Write the equation of the hyperbola with foci at and passing through the point .
14.
The eccentricity of a hyperbola with and is:
1. a)
2. b)
3. c)
4. d)
15.
Find all key features of