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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The equation to a parabola which passes through the intersection of a straight line \[x+y=0\] and the circle \[{{x}^{2}}+{{y}^{2}}+4y=0\] is [Orissa JEE 2005]

    A)            \[{{y}^{2}}=4x\]                         

    B)            \[{{y}^{2}}=x\]

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

    D)            None of these

    Correct Answer: C

    Solution :

               Given \[x+y=0\]     ?..(i)  \[{{x}^{2}}+{{y}^{2}}+4y=0\]          ?.. (ii)                    Solving (i) and (ii), \[x=0\], \[y=0\]; \[x=2\], \[y=-2\] which means parabola pass through (0, 0) and (2, ?2) these points satisfy the parabola \[{{y}^{2}}=2x\].                         


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