#### Find the equation of the hyperbola satisfying the give conditions: Foci (0,Â±13) the conjugate axis is of length 24

$It\;is\;given\;that,\;foci\;(0,\pm13),\;the\;conjugate\;axis\;is\;of\;length\;24\\* Here\;the\;foci\;are\;on\;the\;y-axis.\\*Therefore,\;the\;equation\;of\; the\; hyperbola\;is\;of\;the\;form\;\frac{y^2}{b^2}-\frac{x^2}{a^2}=1\\*Since,\;the\; foci\;are\;(0,\pm13)\\*\Rightarrow ae=c=13\\*Since\;the\;length\;of\;the\; conjugate\;axis\;is\;24,\\*\Rightarrow 2b=24\Rightarrow b=12\\*We\;know\; that\;a^2+b^2=c^2\\*\therefore a^2+12^2=13^2\Rightarrow a^2=169-144= 25\\*Thus\;the\;equation\;of\;the\;hyperbola\;is\;\frac{y^2}{25}-\frac{x^2}{144}=1$