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AP EAMCET201726 Apr 2017Morning ShiftMathematicsDifferential EquationsActual

The differential equation corresponding to the family of circles in the plane touching the Y -axis at the origin, is

Options

  1. Ad y d x = y^2-x^2 2 x y
  2. Bd y d x = 2 x y x^2+y^2
  3. Cd y d x = x^2-y^2 2 x y
  4. Dd y d x = x^2+y^2 2 x y

Correct answer

A. d y d x = y^2-x^2 2 x y

Step-by-step solution

Here, it is given that circle touches the y -axis at origin. So, equation of family of circles (x-a)^2+y^2=a^2 x^2+a^2-2 a x+y^2=a^2 On differentiating w.r.t. x , we get Now, from Eqs. (i) and (ii), we get aligned & x^2+y^2= (2 x+2 y d y d x ) x & x^2+y^2=2 x^2+2 x y d y d x & d y d x = y^2-x^2 2 x y aligned This is the required differential equation.

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