**Problem : **
Is the transverse axis of this hyperbola horizontal or vertical: - + = 1.

Because the

*y*^{2} term is negative, the transverse axis is horizontal.

**Problem : **
Find *a*, *b*, and *c* of the following hyperbola: 5*x*^{2} -3*y*^{2} - 20*x* + 6*y* + 2 = 0.

By completing the square, factoring, and putting the equation in standard
form, it is evident that

*a* = ,

*b* = , and

*c* = .

**Problem : **
The eccentricity of a hyperbola with center (0, 0) and focus 5, 0) is . What is the standard equation for the hyperbola?

*e* = , so

*c* = 5,

*a* = 3, and

*b* = = 4. The
locations of the focus and the center mean that the transverse axis is
horizontal, and the

*y*^{2} term is negative. So the standard equation for this
hyperbola is

- = 1.

**Problem : **
Find the asymptotes of the hyperbola
- = 1.

*a* = ,

*b* = 2. The asymptotes are

*y* = *x* and

*y* = - *x*.

**Problem : **
The transverse axis of a hyperbola is horizontal. One of the asymptotes is *y* = *x* + 5. What is the standard equation of the hyperbola?

*a* = 1,

*b* = 2, and the center of the hyperbola is

(0, 5). The standard
equation, then, is

- = 1.