A) \[\sqrt{10}\]
B) \[\frac{6}{5}\]
C) \[\frac{1}{\sqrt{10}}\]
D) \[\frac{6}{5}\sqrt{10}\]
Correct Answer: D
Solution :
The equations of straight line and hyperbola are respectively \[x-3y=1\] ?(i) and \[{{x}^{2}}-4{{y}^{2}}=1\] ?(ii) On solving Eqs. (i) and (ii), we get \[A\,(1,\,0)\] and \[B\left( -\frac{13}{5},-\frac{6}{5} \right)\] which are the points of intersection of straight line and hyperbola. \[\therefore \] Length of straight line intercepted by the hyperbola\[=\sqrt{{{\left( -\frac{13}{5}-1 \right)}^{2}}+{{\left( -\frac{6}{5} \right)}^{2}}}\] \[=\sqrt{{{\left( -\frac{18}{5} \right)}^{2}}+{{\left( -\frac{6}{5} \right)}^{2}}}\] \[=\sqrt{\frac{324+36}{25}}=\sqrt{\frac{360}{25}}=\frac{6}{5}\sqrt{10}\]
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