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In a linear equation, the independent variable increases at a constant rate while the dependent variable decreases at a constant rate.
Solution:
The standard equation of a hyperbola is expressed as

Given that the hyperbola has its foci at (0,-15) and (0, 15), this implies that the hyperbola is parallel to the y-axis.
Thus, the equation will be expressed in the form:

The asymptote of n hyperbola is expressed as

Given that the asymptotes are

This implies that

To evaluate the value of h and k,
If you want to find out what that number is, then let's call it n
n + 3n (Three times the number) + 12 = 32
Simplify
4n + 12 = 32
Subtract 12 from each side
4n = 20
Divide each side by 4
n = 5
See attached image for work.