Question 1184487
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Then the hyperbola is centered at the origin of the coordinate system,

the transverse semi-axis is along x-axis.


The length of the conjugate semi-axis is b = {{{sqrt(5^2 - 3^2)}}} = 4.


The sought equation of the hyperbola is therefore


    {{{x^2/3^2}}} - {{{y^2/4^2}}} = 1.
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Solved.