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NDA2017MathematicsDifferential EquationsActual

What is the differential equation corresponding to y^2-2 a y+x^2=a^2 by eliminating a ?

Options

  1. A(x^2-2 y^2 ) p^2-4 p x y-x^2=0
  2. B(x^2-2 y^2 ) p^2-4 p x y-x^2=0
  3. C(x^2+2 y^2 ) p^2-4 p x y-x^2=0
  4. D(x^2+2 y^2 ) p^2-4 p x y+x^2=0 where p = dy dx

Correct answer

A. (x^2-2 y^2 ) p^2-4 p x y-x^2=0

Step-by-step solution

aligned & y^2-2 a y+x^2=a^2 & y^2-2(y)(a)+a^2+x^2=a^2+a^2 & (y-a)^2+x^2=2 a^2...(i) aligned Dift w.r.t x aligned & 2(y-a) y^1+2 x=0 & (y-a) p=-x & y-a= -x p ...(ii) & a=y+ x p ...(iii) aligned (i) ( -x p )^2+x^2=2 (y+ x p )^2 aligned & =2 ( ( py + x )^2 p 2 ) & x ^2+ p ^2 x ^2 p ^2 = 2 ( p ^2 y ^2+ x ^2+2 pxy ) p ^2 & x ^2+ p ^2 x ^2-2 p ^2 y ^2-2 x ^2-4 pxy =0 & ( x ^2-2 y ^2 ) p ^2-4 pxy - x ^2=0 aligned

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