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JEE Advanced2007MathematicsDifferential EquationsActual

The differential equation d y d x = 1-y^2 y determines a family of circles with

Options

  1. Avariable radii and a fixed centre at (0,1)
  2. Bvariable radii and a fixed centre at (0,-1)
  3. Cfixed radius 1 and variable centres along the X -axis
  4. Dfixed radius 1 and variable centres along the Y -axis

Correct answer

C. fixed radius 1 and variable centres along the X -axis

Step-by-step solution

aligned & d y d x = 1-y^2 y & y 1-y^2 d y= d x & - 1-y^2 =x+C & (x+c)^2+y^2=1 & aligned Centre (-C, 0) and radius =1 .

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