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JEE Main & Advanced Sample Paper JEE Main Sample Paper-2

  • question_answer
    Directions: Read the fallowing questions and choose: Statement 1: The differential equation \[\frac{dy}{dx}=\frac{\sqrt{1-{{y}^{2}}}}{y}\] determines a family of circles. Statement 2: \[{{x}^{2}}+{{y}^{2}}+2kx+{{k}^{2}}-1=0\] represents a family of circles with fixed radius 1 and variable centres lying along x-axis.

    A)  Both statements are True, Statement-2 explains Statement-1.

    B)  Both statements are True, Statement-2 does not explain Statement-1.

    C)  Statement-1 is True, Statement-2 is False.

    D)  Statement-1 is False, Statement-2 is true.

    Correct Answer: A

    Solution :

    \[\frac{ydy}{\sqrt{1-{{y}^{2}}}}=dx\] \[\Rightarrow \]               \[-\frac{1}{2}\cdot 2\sqrt{1-{{y}^{2}}}=x+c\] \[\Rightarrow \]               \[-\sqrt{1-{{y}^{2}}}=x+c\] \[\Rightarrow \]               \[{{x}^{2}}+{{y}^{2}}+2cx+{{c}^{2}}-1=0\] Centre of \[(-c,\,0),\] radius = 1.


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