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JEE Main & Advanced Mathematics Conic Sections Question Bank Hyperbola

  • question_answer
    The line \[y=mx+c\] touches the curve \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if [Kerala (Engg.) 2002]

    A)            \[{{c}^{2}}={{a}^{2}}{{m}^{2}}+{{b}^{2}}\]                                   

    B)            \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}\]

    C)            \[{{c}^{2}}={{b}^{2}}{{m}^{2}}-{{a}^{2}}\]                                   

    D)            \[{{a}^{2}}={{b}^{2}}{{m}^{2}}+{{c}^{2}}\]

    Correct Answer: B

    Solution :

               \[y=mx+c\] touches the curve \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\], if  \[{{c}^{2}}={{a}^{2}}{{m}^{2}}-{{b}^{2}}.\]


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