JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The ends of the latus rectum of the conic \[{{x}^{2}}+10x-16y+25=0\] are                                         [Karnataka CET 2005]

    A)            (3, ?4), (13, 4)                           

    B)            (?3, ?4), (13, ?4)

    C)            (3, 4), (?13, 4)                           

    D)            (5, ?8), (?5, 8)

    Correct Answer: C

    Solution :

               Equation of conic is \[{{x}^{2}}+10x-16y+25=0\] i.e., \[{{(x+5)}^{2}}=16y\].                    \ Conic is parabola with focus (?5, 4)                    \[\because \] focus is mid point of latus rectum.                    \ only points given in option (c) can be end points of the latus rectum.


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