KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • question_answer
    The radius of an arc given by locus of z if arc \[\left( \frac{z-4i}{z-3} \right)=\frac{\pi }{3}\] is

    A) \[5\sqrt{3}\]                  

    B) \[3\sqrt{5}\]

    C) \[\frac{5}{\sqrt{3}}\]     

    D) \[\frac{5}{2}\]

    Correct Answer: C

    Solution :

    [c] We have, \[\arg \left( \frac{z-4i}{z-3} \right)=\frac{\pi }{3}\] In \[\Delta OAB,\] \[\cos \frac{2\pi }{3}=\frac{O{{A}^{2}}+O{{B}^{2}}-A{{B}^{2}}}{2OA\cdot OB}\] \[\Rightarrow \]   \[\frac{-1}{2}=\frac{2{{r}^{2}}-25}{2{{r}^{2}}}\]\[\Rightarrow \]\[3{{r}^{2}}=25\] \[r=\frac{5}{\sqrt{3}}\]             

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