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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The equation of a tangent to the parabola \[{{y}^{2}}=4ax\] making an angle \[\theta \] with x-axis is

    A)            \[y=x\cot \theta +a\tan \theta \]    

    B)            \[x=y\tan \theta +a\cot \theta \]

    C)            \[y=x\tan \theta +a\cot \theta \]    

    D)            None of these

    Correct Answer: C

    Solution :

               \[m=\tan \theta \]. The tangent to \[{{y}^{2}}=4ax\] is \[y=x\tan \theta +c\]            Hence \[c=\frac{a}{\tan \theta }=a\cot \theta \]            \ The equation of tangent is \[y=x\tan \theta +a\cot \theta \].


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