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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2004

  • question_answer
    If tangent to the curve \[x=a{{t}^{2}},y=2at\] is perpendicular to x-axis, then its point of contact is :

    A)  \[(a,\,a)\]                          

    B)  \[(0,\,a)\]

    C)  \[(0,0)\]                             

    D)  \[(0,0)\]

    Correct Answer: C

    Solution :

    We have, \[x=a\,{{t}^{2}}\] \[\therefore \]  \[\frac{dx}{dt}=2at\] and  \[y=2at\Rightarrow \frac{dy}{dt}=2a\] \[\therefore \] tangent \[\left( \frac{dy}{dx} \right)=\frac{2a}{2at}=1/t\] \[\Rightarrow \,\frac{1}{t}=\infty \] \[\Rightarrow t=0\Rightarrow \] points of contact is (0, 0).


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