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KVPY Sample Paper KVPY Stream-SX Model Paper-6

  • question_answer
    The area of rhombus formed by foci of hyperbola \[9{{x}^{2}}-16{{y}^{2}}=144\] and its conjugate hyperbola is

    A) \[\frac{75}{8}\]                         

    B) 50

    C) \[\frac{75}{2}\]

    D)                                \[\frac{75}{4}\]

    Correct Answer: B

    Solution :

    \[a=4,\]\[e=\frac{5}{4}\] \[\therefore \]      foci are \[(\pm \,\,5,\,\,0)\]             Equation of the conjugate hyperbola is \[16{{y}^{2}}-9{{x}^{2}}=144\] its foci are \[(0,\,\,\pm 5)\] \[\therefore \]      area of the rhombus = 50


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