A) \[\frac{75}{\sqrt{7}}\]
B) \[\frac{150}{\sqrt{7}}\]
C) \[\frac{75}{\sqrt{14}}\]
D) None of these
Correct Answer: C
Solution :
Tangent to\[9{{x}^{2}}-16{{y}^{2}}=144\]is \[y=mx\pm \sqrt{16{{m}^{2}}-9}.\] Since it touches circle also \[\therefore \] \[\frac{\sqrt{16{{m}^{2}}-9}}{\sqrt{1+{{m}^{2}}}}=3\]or\[16{{m}^{2}}-9=9+9{{m}^{2}}\]or\[{{m}^{2}}=\frac{18}{7}\]Equation of tangent \[y=\pm 3\sqrt{\frac{2}{7}}x\pm \frac{15}{\sqrt{7}}\]
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