Manipal Engineering Manipal Engineering Solved Paper-2011

  • question_answer
    The degree and order of the differential equation of the family of all parabolas whose axis is x-axis, are respectively

    A)  2, 1                                       

    B)  1, 2

    C)  3, 2                       

    D)         2, 3

    Correct Answer: A

    Solution :

    Let the equation of parabola whose axis is\[x-\]axis, is                 \[{{y}^{2}}=\pm 4a(x-h)\] On differentiating w.r.t. x, we get                 \[2y{{y}_{1}}=\pm \,4a\] \[\Rightarrow \]               \[y{{y}_{1}}=\pm 2a\] Again differentiating, we get                 \[{{({{y}_{1}})}^{2}}+y{{y}_{2}}=0\] Hence, order and degree are respectively 1 and 2.


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