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The length of the conjugate axis of the hyperbola $9 x^{2} - 16 y^{2} - 18 x - 64 y + 89 = 0$ is

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Detailed Solution

$\begin{array}{l} 9 x^{2} - 16 y^{2} - 18 x - 64 y + 89 = 0 \\ 9 (x^{2} - 2 x + 1) - 9 - 16 (y^{2} + 4 y + 4) + 64 = - 89 \\ 9 {(x - 1)}^{2} - 16 {(y + 2)}^{2} = - 144 \\ \frac{{(x - 1)}^{2}}{16} - \frac{{(y + 2)}^{2}}{9} = - 1 \end{array}$

Length of conjugate axis is $2 b = 6$

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