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JEE Main & Advanced Mathematics Differential Equations Question Bank Self Evaluation Test - Differential Equations

  • question_answer
    The differential equation which represents the three parameter family of circles\[{{x}^{2}}+{{y}^{2}}+2gx+2fy+c=0\] is

    A) \[y'''=\frac{3y'y'{{'}^{2}}}{1+y{{'}^{2}}}\]   

    B) \[y'''=\frac{3y'{{'}^{2}}}{1+y{{'}^{2}}}\]

    C) \[y'''=\frac{3y'}{1+y{{'}^{2}}}\]

    D) \[y'''=\frac{3y'}{1-y{{'}^{2}}}\]

    Correct Answer: A

    Solution :

    [a] To eliminate the parameters g, f and c differentiate thrice w.r.t. x, \[x+yy'+g+fy'=0\]                                 ? (1) \[1+y{{'}^{2}}+yy''+fy''=0\]                            ? (2) \[3y'y''+yy'''+fy'''=0\]                              ? (3) (1) \[y'''-(2)y''\] gives,


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