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MHT CET202310 May 2023Morning ShiftMathematicsDifferential EquationsActual

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

Options

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

Correct answer

D. fixed radius of 1 unit and variable centre along the X -axis.

Step-by-step solution

array ll & d y ~d x = 1-y^2 y & y 1-y^2 ~d y= 1 ~d x & - 1-y^2 =x+ c & (x+ c )^2=1-y^2 array (x+ c )^2+y^2=1 Radius is fixed, which is 1 and the centre is (-c, 0) which is a variable centre on the X -axis.

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