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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    If \[4{{x}^{2}}+p{{y}^{2}}=45\] and \[{{x}^{2}}-4{{y}^{2}}=5\] cut orthogonally, then the value of p is               [Kerala (Engg.) 2005]

    A)            1/9 

    B)            1/3

    C)            3     

    D)            18

    E)            9

    Correct Answer: E

    Solution :

                      Slope of 1st curve \[{{\left( \frac{dy}{dx} \right)}_{I}}=-\frac{4x}{py}\]                   Slope of 2nd curve \[{{\left( \frac{dy}{dx} \right)}_{II}}=\frac{x}{4y}\]                   For orthogonal intersection \[\left( -\frac{4x}{py} \right)\,\left( \frac{x}{4y} \right)=-1\]                   Þ \[{{x}^{2}}=p{{y}^{2}}\]                   On solving equations of given curves \[x=3\], \[y=1\]                    \ \[p(1)={{(3)}^{2}}=9\] Þ \[p=9\].


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