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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The point of the contact of the tangent to the parabola \[{{y}^{2}}=4ax\] which makes an angle of \[{{60}^{o}}\]with x-axis, is

    A)            \[\left( \frac{a}{3},\ \frac{2a}{\sqrt{3}} \right)\]                       

    B)            \[\left( \frac{2a}{\sqrt{3}},\ \frac{a}{3} \right)\]

    C)            \[\left( \frac{a}{\sqrt{3}},\ \frac{2a}{3} \right)\]                       

    D)            None of these

    Correct Answer: A

    Solution :

               \[m=\tan \theta =\tan 60{}^\circ =\sqrt{3}\]            The equation of tangent at \[(h,k)\] to \[{{y}^{2}}=4ax\] is \[yk=2a(x+h)\]            Comparing, we get \[m=\sqrt{3}=\frac{2a}{k}\] or \[k=\frac{2a}{\sqrt{3}}\] and \[h=\frac{a}{3}\].


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