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Grade 12Differential Calculus

The form of the differential equation of the central conics, is
A . x = y dy/dx
  1. x+y dy/dx= 0
  2. x (dy/dx)2 +xy (d2x/dx2)= y(dy/dx)
  3. none of these

Profile image of Riya Das
7 Years agoGrade 12
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1 Answer

Profile image of kkbisht
7 Years ago
Let the equation of the Central Conic is ax2 +by2=1
differentiating w.r.t.  x we obtain   2ax + 2bydy/dx =0 => ax+bydy/dx =0 => a/b   + y/x (dy/dx)=0 -----(1) 
further differentiating w. r.t, x we get a + b (y (d2y/dx2) + (dy/dx)2 =0 using  (1) and simplifying we finally get 
x(dy/dx)2  +xy(d2y/dx2)= y(dy/dx)
So option(3) is correct
kkbisht
 

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