Math  /  Geometry

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Find the center of the hyperbola defined by the equation (y4)236(x4)249=1\frac{(y-4)^{2}}{36}-\frac{(x-4)^{2}}{49}=1. If necessary, round to the nearest tenth.
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Studdy Solution
Determine the center of the hyperbola from the equation:
Given equation:
(y4)236(x4)249=1\frac{(y-4)^{2}}{36} - \frac{(x-4)^{2}}{49} = 1
Compare with the standard form:
(yk)2a2(xh)2b2=1\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1
From comparison, we identify:
k=4k = 4 and h=4h = 4
Thus, the center of the hyperbola is (h,k)=(4,4)(h, k) = (4, 4).
The center of the hyperbola is:
(4,4)\boxed{(4, 4)}

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