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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The centroid of the triangle formed by joining the feet of the normals drawn from any point to the parabola \[{{y}^{2}}=4ax\], lies on [MP PET 1999]

    A)            Axis                                           

    B)            Directrix

    C)            Latus rectum                             

    D)            Tangent at vertex

    Correct Answer: A

    Solution :

               Normal to parabola will be, \[y=mx-2am-a{{m}^{3}}\]            For three values of m. Three normal can be drawn on parabola\[{{y}^{2}}=4ax\]. So three feet of normals can be obtained, hence centroid of triangle lies on axis of parabola.


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