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__Given__A hyperbola with center at (4, 5), vertices at (0, 5) and (8, 5), b=2. The equation for a hyperbola with center (h, k) is ((x-h)/a)^2 - ((y-k)/b)^2 = 1.__Find__The equation for the given hyperbola.__Solution__We can write most of the equation immediately by substituting the given numbers. We know that the equation is satisfied at the vertices, so we can find "a" by ((0-4)/a)^2 - ((5-5)/2)^2 = 1 The second term is zero, so the first term must be 1. By inspection, a=4. The equation of the hyperbola is**((x-4)/4)^2 - ((y-5)/2)^2 = 1**.