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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2005

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

    A)  (0, 0)             

    B)  (0, a)

    C)  (a, 0)             

    D)  (a, a)

    Correct Answer: A

    Solution :

     Given, curve is \[x=a{{t}^{2}},\text{ }y=2at\] \[\Rightarrow \] \[\frac{dx}{dt}=2at,\frac{dy}{dt}=2a\] \[\therefore \] \[\frac{dx}{dy}=\frac{2at}{2a}=t\] \[\because \]Tangent line is perpendicular to\[x-\]axis. \[\therefore \] \[\frac{dx}{dy}=0\] \[\Rightarrow \] \[t=0\] Hence, point of contact is (0, 0).


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