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MHT CET20243 May 2024Morning ShiftMathematicsCircleActual

The differential equation of family of circles, whose centres are on the X -axis and also touch the Y -axis is

Options

  1. A4 (x+y ~d y ~d x )^2 x^2= (x^2+y^2 )^2
  2. B(x+y ~d y ~d x )^2 x^2= (x^2+y^2 )^2
  3. C2 (x+y ~d y ~d x )^2 x^2= (x^2+y^2 )^2
  4. D(x+y ~d y ~d x )^2 x^2=4 (x^2+y^2 )^2

Correct answer

A. 4 (x+y ~d y ~d x )^2 x^2= (x^2+y^2 )^2

Step-by-step solution

The system of circles whose centre lies on X -axis and touch Y -axis (i.e., passes through the origin) is x^2+y^2=2 ~b x...(i) Differentiating w.r.t x , we get x+y ~d y ~d x = b ...(ii) Substituting (ii) in (i), we get aligned & x^2+y^2=2 (x+y ~d y ~d x ) x & (x^2+y^2 )^2=4 (x+y ~d y ~d x )^2 x^2 aligned

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