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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The locus of a foot of perpendicular drawn to the tangent of parabola \[{{y}^{2}}=4ax\] from focus, is           [RPET 1989]

    A)            \[x=0\]                                      

    B)            \[y=0\]

    C)            \[{{y}^{2}}=2a(x+a)\]                

    D)            \[{{x}^{2}}+{{y}^{2}}(x+a)=0\]

    Correct Answer: A

    Solution :

               Tangent to parabola is, \[y=mx+\frac{a}{m}\]          .....(i)                    A line perpendicular to tangent and passing from focus \[(a,\,0)\] is, \[y=-\frac{x}{m}+\frac{a}{m}\]                                .....(ii)                    Solving both lines (i) and (ii) Þ \[x=0\].


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