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What is the equation of an ellipse whose center is at the point \(\left(5,4\right)\), foci are at the points \(\left(0,4\right)\; {\rm and}\; \left(10,4\right)\), and endpoints of the major axis at the points \(\left(-3,4\right)\; {\rm and}\; \left(13,4\right)?\) Enter your answer in the form \(\frac{\left(x-h\right)^{2} }{a\_ ^{2} } +\frac{\left(y-k\right)^{2} }{b\_ ^{2} } =1.\)
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