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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        The order of the differential equation of all tangent lines to the parabola\[y={{x}^{2}}\]is

    A)  1                            

    B)  2

    C)  3                            

    D)  4

    Correct Answer: A

    Solution :

                    The parametric form of the given equation is \[x=t\]and\[y={{t}^{2}}\]. The equation of any tangent at t is\[2xt=y+{{t}^{2}}\] On differentiating, we get\[2t={{y}_{1}}\] On putting this value in the equation of tangent, we have                 \[\frac{2x{{y}_{1}}}{2}=y+{{\left( \frac{{{y}_{1}}}{2} \right)}^{2}}\] \[\Rightarrow \]               \[4x{{y}_{1}}=4y+y_{1}^{2}\] So, the order of this equation is one.


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