The hyperbola with center at (4, 5), with vertices at (0, 5) and (8, 5), with b = 2.

The standard form of hyperbola is:

(x-h) ²/a² - (y-k) ²/b²=1

center: (4,5)

Length of the horizontal transverse axis: 8-5=3=2a

thus

a=3/2

a²=9/4

b=2

b²=4

Hence the equation will be:

(x-4) ² / (9/4) - (y-5) ²/4=1

simplifying this we get:

[4 (x-4) ²]/9 - (y-5) ²/4=1