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VIT Engineering VIT Engineering Solved Paper-2009

  • question_answer
    If the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] intersects the hyperbola\[xy={{c}^{2}}\]in four points \[({{x}_{i}},\,{{y}_{i}}),\]for \[i=\] 1, 2, 3 and 4, then \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}\] equals

    A)  0              

    B)  \[c\]

    C)  \[a\]                

    D)  \[{{c}^{4}}\]

    Correct Answer: A

    Solution :

    Given,            \[{{x}^{2}}{{y}^{2}}={{c}^{4}}\] \[\Rightarrow \] \[{{y}^{2}}({{a}^{2}}-{{v}^{2}})={{c}^{4}}\] \[\Rightarrow \] \[{{y}^{2}}-{{a}^{2}}{{y}^{2}}+{{c}^{4}}=0\] Let \[{{y}_{1}},{{y}_{2}},{{y}_{3}}\] and \[{{y}_{4}}\] are the roots. \[\therefore \] \[{{y}_{1}}+{{y}_{2}}+{{y}_{3}}+{{y}_{4}}=0\]


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