Equation of hyperbola vertices (4, -14) and (4, 10) asyptotes y=4x-18 and y=-4x+14?

Question

I do not understand how to find the b value....So far I have a center of (4, -2) a=6... please help.

Answer 1

You are correct about the center, but a is half the distance between the vertices:
a = 24/2 = 12
An important clue is that the slope of the asymptotes are:
+/- b/a
In this case the slope of the asymptotes is +/-4 so:
b/12 = 4
b = 48
Since the major axis is vertical, the equation takes this form:
[(y + 2)^2]/12 - [(x - 4)^2]/48 = 1