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MHT CET202121 Sep 2021Evening ShiftMathematicsDifferential EquationsActual

The differential equation of the family of circles touching 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

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

Step-by-step solution

Since circles touch Y axis at origin, the centres of the circles lie on X axis. Let centre be ( h , 0) and radius = h ( x - h )^2+( y -0)^2= h ^2 x ^2-2 hx + y ^2=0 Differentiating w.r.t. x , we get 2 x-2 h+2 y d y d x =0 x+y d y d x =h Substituting value of h in eq. (1), we get aligned & x^2-2 (x+y d y d x ) x+y^2=0 & x^2-2 x^2-2 x y d y d x +y^2=0 x^2-y^2+2 x y d y d x =0 aligned

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