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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    The product of the lengths of perpendiculars drawn from any point on the hyperbola \[{{x}^{2}}-2{{y}^{2}}-2=0\] to its asymptotes is [EAMCET 2003]

    A)            1/2 

    B)            2/3

    C)            3/2 

    D)            2

    Correct Answer: B

    Solution :

                      Given equation is \[\frac{{{x}^{2}}}{2}-\frac{{{y}^{2}}}{1}=1\]                    .....(i)                    Product of length of perpendiculars drawn from any point on the hyperbola (i) to the asymptotes is \[\frac{{{a}^{2}}{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}=\frac{2\times 1}{2+1}=\frac{2}{3}\].


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