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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The equation of latus rectum of a parabola is \[x+y=8\] and the equation of the tangent at the vertex is \[x+y=12\], then length of the latus rectum is                                                                                            [MP PET 2002]

    A)            \[4\sqrt{2}\]                             

    B)            \[2\sqrt{2}\]

    C)            8     

    D)            \[8\sqrt{2}\]

    Correct Answer: D

    Solution :

               Clearly; \[a=\left| \frac{-8}{\sqrt{1+1}} \right|-\,\left| \frac{-12}{\sqrt{1+1}} \right|=\frac{4}{\sqrt{2}}\]            Length of latus rectum = 4a \[=4\times \frac{4}{\sqrt{2}}=8\sqrt{2}\].


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