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JEE Main & Advanced JEE Main Paper (Held On 22 April 2013)

  • question_answer
    Statement 1: The line \[x-2y=2\] meets the parabola, \[{{y}^{2}}+2x=0\] only at the point \[(-2,-2):\]                 Statement 2: The line \[y=mx-\frac{1}{2m}(\operatorname{m}\#0)\]is tangent to the parabola, \[{{y}^{2}}=-2x\] at the point \[\left( -\frac{1}{2{{\operatorname{m}}^{2}}},\frac{1}{\operatorname{m}} \right).\]     JEE Main  Online Paper (Held On 22 April 2013)

    A)  Statement 1 is true; Statement 2 is false.

    B)  Statement 1 is true; Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

    C)  Statement 1 is false; Statement 2 is true.

    D)  Statement 1 is true; Statement 2 is true; Statement 2 is not a correct explanation for Statement 1.

    Correct Answer: B

    Solution :

     Both statements are true and statement-2 is the correct explanation of statement-1 \[\therefore \] The straight line \[y=mx+\frac{a}{m}\] is always a tangent to the parabola \[{{y}^{2}}=4ax\] for any value of m. The co-ordinates of point of contact \[\left( \frac{a}{{{m}^{2}}},\frac{2a}{m} \right)\]


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