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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    At what point on the parabola \[{{y}^{2}}=4x\], the normal makes equal angles with the co-ordinate axes     [RPET 1994]

    A)            (4, 4)                                         

    B)            (9, 6)

    C)            (4, ?4)                                       

    D)            (1, ?2)

    Correct Answer: D

    Solution :

               The equation of a normal to \[{{y}^{2}}=4x\]at \[({{m}^{2}},-2m)\] is \[y=mx-2m-{{m}^{3}}.\] If the normal makes equal angles with the coordinates axes, then \[m=\tan \frac{\pi }{4}=1.\] Thus, the required point is (1, ? 2).


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