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AP EAMCET20226 Jul 2022Morning ShiftMathematicsDifferential EquationsActual

The solution of (1+y^2 ) d x-x y d y=0, y(1)=0 represents a conic. Its eccentricity is

Options

  1. A2
  2. B1 / e
  3. C1
  4. D2

Correct answer

D. 2

Step-by-step solution

Given (1+y^2 ) d x-x y d y-0 and y(1)=0 . Take, (1+y^2 ) d x-x y d y=0 d x (1+y^2 )=x y d y d x x = y d y d+y^2 aligned & ydy = 1 2 dt & x = 1 2 dt t & x = 1 2 t + c & x = ( t c ) aligned aligned & x= 1+y^2 c & Put x=1, y=0 & 1= 1 c & c=1 aligned Then, x= 1+y^2 aligned & x^2-y^2=1 & a=b=1 & c= 1+1 = 2 aligned So, e = c a = 2 l = 2 .

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