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JEE Main & Advanced Mathematics Conic Sections Question Bank Parabola

  • question_answer
    The length intercepted by the curve \[{{y}^{2}}=4x\] on the line satisfying \[dy/dx=1\] and passing through point (0, 1) is given by [Orissa JEE 2005]

    A)            1     

    B)            2

    C)            0     

    D)            None of these

    Correct Answer: C

    Solution :

               Let equation of line is \[y=ax+b\];  \ \[\frac{dy}{dx}=a=1\] given                    Also \[y=ax+b\] passing through (0, 1) \ \[b=1\]                    So required line be \[y=x+1\]                    Now point of intersection of the line and parabola gives \[{{x}^{2}}+2x+1=4x\] Þ \[{{x}^{2}}-2x+1\] Þ \[x=1\] \ \[y=2\]                    \ Line touch that parabola.                    \ Length intercepted is equal to 0.


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