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MHT CET2010MathematicsDifferential Equations

The differential equation of family of circles whose centre lies on x -axis, is

Options

  1. Ad² y d x² + ( d y d x )²+1=0
  2. By d² y d x² + ( d y d x )²-1=0
  3. Cy d² y d x² - ( d y d x )²-1=0
  4. Dy d² y d x² + ( d y d x )²+1=0

Correct answer

D. y d² y d x² + ( d y d x )²+1=0

Step-by-step solution

The equation of family of circle having centre at x -axis is x²+y²-2 a x=0 . On differentiating, we get 2 x+2 y d y d x -2 a=0 Again, differentiating, we get aligned & 2+2 [y d² y d x² + ( d y d x )² ]=0 & y d² y d x² + ( d y d x )²+1=0 aligned

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