Please help me solve this problem: The hyperbola with center at (4,5) with vertices at (0,5) and (8,5) with b=2?


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We assume you have 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.

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