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AP EAMCET20227 Jul 2022Morning ShiftMathematicsDifferential EquationsActual

The differential equation of the family of circles passing through (0,0) and having centre on X -axis is

Options

  1. A2 x y d y d x +x^2-y^2=0
  2. B( d y d x )^2+y d^2 y d x^2 +1=0
  3. Cx y d y d x +y^2-x^2=0
  4. Dd y d x = x+y x-y

Correct answer

A. 2 x y d y d x +x^2-y^2=0

Step-by-step solution

Equation of family of circle (x-r)^2+y^2=r^2 . ...(i) On differentiating w.r.t. x , 2(x-r)+2 y y^ =0 (x-r)+y y^ =0 aligned & r=x+y y^ & From Eq. (i), aligned (x-x-y y^ )^2+y^2= (x+y y^ )^2 array ll & (y y^ )^2+y^2=x^2+ (y y^ )^2+2 x y y^ & 2 x y y^ +x^2-y^2=0 array i.e. 2 x y d y d x +x^2-y^2=0

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