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JEE Main & Advanced Sample Paper JEE Main Sample Paper-9

  • question_answer
    The figure below shows a right triangle with its hypotenuse OB along the y-axis and its vertex A on the parabola \[y={{x}^{2}}.\] Let h represents the length of the hypotenuse which depends on the x-coordinate of the point A. The value of \[\underset{x\to 0}{\mathop{\lim }}\,(h)\] equals

    A)  0                                            

    B) \[\frac{1}{2}\]      

    C)  1                            

    D)  2

    Correct Answer: C

    Solution :

    Let the point \[A=(t,{{t}^{2}});{{m}_{OA}}=t;\]\[{{m}_{AB}}=-\frac{1}{t}\] Equation of \[AB,y-{{t}^{2}}=-\frac{1}{t}(x-{{t}^{2}})\] On putting x = 0, we get \[h={{t}^{2}}+1\](as\[x\to 0\]then \[t\to 0\]) Now,\[\underset{t\to 0}{\mathop{\lim }}\,(h)=\underset{t\to 0}{\mathop{\lim }}\,(1+{{t}^{2}})=1\]


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