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JEE Main & Advanced Mathematics Conic Sections Question Bank Conic section - General

  • question_answer
    The equation of the conic with focus at (1, ?1), directrix along \[x-y+1=0\] and with eccentricity \[\sqrt{2}\] is [EAMCET 1994]

    A)            \[{{x}^{2}}-{{y}^{2}}=1\] 

    B)            \[xy=1\]

    C)            \[2xy-4x+4y+1=0\]            

    D)            \[2xy+4x-4y-1=0\]

    Correct Answer: C

    Solution :

               Let P (x, y) be any point on the conic. Then \[\sqrt{{{(x-1)}^{2}}+{{(y+1)}^{2}}}=\sqrt{2}\left( \frac{x-y+1}{\sqrt{2}} \right)\], [Using \[SP=e.PM]\]                    \[\Rightarrow 2xy-4x+4y+1=0\].


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