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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
     If PSQ is the focal chord of the parabola \[{{y}^{2}}=8x\] such that\[SP=6\]. Then the length SQ is

    A)            6     

    B)            4

    C)            3     

    D)            None of these

    Correct Answer: C

    Solution :

               Since the semi-latus rectum of a parabola is the harmonic mean between the segments of any focal chord of a parabola, therefore \[SP,\,\,4,\,\,SQ\]are in H.P.                    \[\Rightarrow 4=2.\frac{SP.SQ}{SP+SQ}\Rightarrow 4=\frac{2(6)(SQ)}{6+SQ}\Rightarrow SQ=3\].


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