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AP EAMCET2014MathematicsDifferential Equations

The differential equation of the family of parabolas with vertex at (0,-1) and having axis along the Y -axis is

Options

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

Correct answer

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

Step-by-step solution

Equation of family of parabola having vertex (0,-1) and axis along y -axis is x^2=4 a(y+1) On differentiating both sides w.r.t. x , we get 2 x=4 a y^ a= x 2 y^ On putting a= 1 2 y^ in Eq. (i), we get array cc & x^2=4 x 2 y^ (y+1) & x= 2 y^ (y+1) & x y^ -2 y-2=0 array

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