KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    The curve amongst the family of curves represented by the differential equation, \[({{x}^{2}}-{{y}^{2}})dx+2xy\]\[dy=0\] which passes through \[(1,1),\] is:

    A) a circle with centre on the \[x\]-axis

    B) an ellipse with major axis along the\[y\]-axis

    C) a circle with centre on the \[y\]-axis

    D) a hyperbola with transverse axis along the\[x\]-axis

    Correct Answer: A

    Solution :

    \[dx=-\left( \frac{x.2ydy-{{y}^{2}}dx}{{{x}^{2}}} \right)\]
    Integrals          \[x=-\frac{{{y}^{2}}}{x}+c\]

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