Question

Find the equation of the hyperbola whose foci are (0,± 5), the transverse axis is of length 3

Answer 1

$Since\: the \:foci\: are\: (±5, 0), c = 5.\\Since\: the\: length\: of \:the\: transverse\: axis\: is \:8, 2a = 8 \\ a = 4.\\We\: know\: that\: a^{2} + b^{2} = c^{2} \\therefore\:4^{2} + b^{2} = 5^{2} \\ b^{2} = 25 -16\\= 9$

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