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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    If the line \[y=mx+c\] is a tangent to the parabola \[{{y}^{2}}=4a(x+a)\] then \[ma+\frac{a}{m}\] is equal to

    A)            c     

    B)            2c

    C)            ? c  

    D)            3c

    Correct Answer: A

    Solution :

               Tangent at \[{{y}^{2}}=4ax\]is \[y=mx+\frac{a}{m}\]            Therefore, tangent at \[{{y}^{2}}=4a(x+a)\] is,            \[y=m(x+a)+\frac{a}{m}\]            or \[y=mx+ma+\frac{a}{m}\]Þ\[ma+\frac{a}{m}=c\].


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