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NDA2019MathematicsDifferential EquationsActual

The differential equation of the system of circles touching the y -axis at the origin is

Options

  1. Ax^2+y^2-2 x y d y d x =0
  2. Bx^2+y^2+2 x y d y d x =0
  3. Cx^2-y^2+2 x y d y d x =0
  4. Dx^2-y^2-2 x y d y d x =0

Correct answer

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

Step-by-step solution

The equation of circle touching y -axis at origin is aligned & (x- )^2+(y-0)^2= ^2 & x^2+ ^2-2 x+y^2= ^2 & x^2+y^2-2 x=0 & x+ y^2 x -2 =0 aligned Differentiating, 1+ x 2 y d y d x -y^2 x^2 =0 x^2+2 x y d y d x -y^2=0

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