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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The tangent to the parabola \[{{y}^{2}}=4ax\] at the point (a, 2a) makes with x-axis an angle equal to           [SCRA 1996]

    A)            \[\frac{\pi }{3}\]                       

    B)            \[\frac{\pi }{4}\]

    C)            \[\frac{\pi }{2}\]                       

    D)            \[\frac{\pi }{6}\]

    Correct Answer: B

    Solution :

               The equation of the tangent at point \[(a,\,2a)\] of the parabola \[{{y}^{2}}=4ax\] is \[y{{y}_{1}}=2a(x+{{x}_{1}})\]                    Þ \[2ay=2a(x+a)\] Þ \[y=x+a\]            This line makes an angle of \[\pi /4\]with the x-axis, as\[m=\tan \theta =1\].


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