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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The equation of the tangent at a point \[P(t)\] where ?t? is any parameter to the parabola \[{{y}^{2}}=4ax\], is             [MNR 1983]

    A)            \[yt=x+a{{t}^{2}}\]                    

    B)            \[y=xt+a{{t}^{2}}\]

    C)            \[y=xt+\frac{a}{t}\]                   

    D)            \[y=tx\]

    Correct Answer: A

    Solution :

               Any point on \[{{y}^{2}}=4ax\]is\[(a{{t}^{2}},\,2at)\], then tangent is\[2aty=2a(x+{{t}^{2}})\]Þ \[yt=x+a{{t}^{2}}\].


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