Which of the following is true for horizontal hyperbolas?

A horizontal hyperbola has its standard form represented as ((y-k)^2/a^2 - (x-h)^2/b^2 = 1), where (a^2) and (b^2) are positive constants, and the (x^2) term appears with a negative sign while the (y^2) term appears with a positive sign. This reflects that the hyperbola opens to the left and right, illustrating that the focus lies along the horizontal axis.

The correct choice indicates that in the context of identifying and defining the shape of the hyperbola, the positive sign correlating with the (y^2) term is vital. In particular, for horizontal hyperbolas, it is the configuration of their equations that reveals important characteristics about their orientations and the nature of the asymptotes. By understanding this standard form, you can accurately derive properties of the hyperbola, including its center location and asymptotic behavior.

In contrast, the other statements do not hold true for horizontal hyperbolas. For instance, claiming that the (y^2) term is positive would correspond to the vertical nature of hyperbolas. Complex asymptotes would invalidate the characteristics of hyperbol