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If you plot the points given on a coordinate plane you see that this is a hyperbola that is is horizontal in nature, meaning it opens side to side, not up and down. We can determine the center of it by taking the point equidistant from the vertices, which is (4, 5), the h and k of our center, respectively. Also, the equation looks like this when it is horizontal: 
. a is the distance between the center and the vertices, so our a = 2, and c is the distance between the center and the foci, so our c = 3. We need to find b now, using Pythagorean's theorem. 
and 
. Now we have everything we need to rewrite the equation: 
If a right triangle has equal legs, it is by definition a 45-45-90 triangle. So, the two sides would be x and the hypotenuse would . However, we know the hypotenuse, and we do not see a
anywhere. That means it has already been multiplied by it, so to get the lengths of the sides we simply divide 26 by
. If you have to rationalize the denominator, the answer will be