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JEE Main2008MathematicsDifferential EquationsActual

The differential equation of the family of circles with fixed radius 5 units and centre on the line y=2 is

Options

  1. A(x-2) y^ 2 =25-(y-2)^2
  2. B(y-2) y^ 2 =25-(y-2)^2
  3. C(y-2)^2 y^ 2 =25-(y-2)^2
  4. D(x-2)^2 y^ 2 =25-(y-2)^2

Correct answer

C. (y-2)^2 y^ 2 =25-(y-2)^2

Step-by-step solution

aligned & (x-h)^2+(y-2)^2=25 & 2(x-h)+2(y-2) d y d x =0 & (x-h)=-(y-2) d y d x aligned substituting in (1), we have aligned & (y-2)^2 ( d y d x )^2+(y-2)^2=25 & (y-2)^2 y^ 2 =25-(y-2)^2 aligned

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