A) \[\frac{9}{2}\]
B) \[-\frac{9}{2}\]
C) \[\frac{32}{3}\]
D) \[-\frac{32}{3}\]
Correct Answer: A
Solution :
Given equation of hyperbola is, \[9{{x}^{2}}-16{{y}^{2}}+72x-32y-16=0\] Þ \[9\,({{x}^{2}}+8x)-16\,({{y}^{2}}+2y)-16=0\] Þ \[9\,{{(x+4)}^{2}}-16{{(y+1)}^{2}}=144\] Þ \[\frac{{{(x+4)}^{2}}}{16}-\frac{{{(y+1)}^{2}}}{9}=1\] Therefore, latus rectum = \[\frac{2{{b}^{2}}}{a}=2\times \frac{9}{4}=\frac{9}{2}\].
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