What are the asymptotes of a vertical hyperbola in terms of y?

For a vertical hyperbola, the standard form of the equation is given as ((x - h)^2/b^2 - (y - k)^2/a^2 = -1). The asymptotes of such a hyperbola are derived from the equation and reflect the way the hyperbola opens.

To determine the equations of the asymptotes for a vertical hyperbola, we recognize that they occur at the points where the hyperbola approaches as (x) and (y) increase or decrease without bound. The asymptotes of a vertical hyperbola are linear equations described by:

[ y - k = \pm \frac{a}{b}(x - h) ]

This can be rearranged to show that the asymptotes are indeed of the form:

[ y = \pm \frac{a}{b}(x - h) + k ]

In this form, (h) represents the horizontal shift (the x-coordinate of the center of the hyperbola), (k) is the vertical shift (the y-coordinate of the center), and the slope (\frac{a}{b}) indicates the steepness of the asymptotes.

Thus, the correct answer, which captures