A) 1
B) 2
C) 3
D) None of these
Correct Answer: A
Solution :
We have, \[a(x-y)=\sqrt{1-{{y}^{2}}}+\sqrt{1-{{x}^{2}}}\] Putting\[x=sin\text{ }A,\text{ }y=sin\text{ }B,\]we get \[cos\text{ }A+cos\text{ }B=a(sin\text{ }A-sin\text{ }B)\] \[\Rightarrow \] \[\cot \frac{A-B}{2}=a\] \[\Rightarrow \] \[A-B=2{{\cot }^{-1}}a\] \[\Rightarrow \] \[{{\sin }^{-1}}x-{{\sin }^{-1}}y=2{{\cot }^{-1}}a\] On differentiating w.r.t.\[x,\]we get \[\frac{1}{\sqrt{1-{{x}^{2}}}}-\frac{1}{\sqrt{1-{{y}^{2}}}}\frac{dy}{dx}=0\] \[\Rightarrow \] \[\frac{dy}{dx}=\frac{\sqrt{1-{{y}^{2}}}}{1-{{x}^{2}}}\] Clearly, it is differential equation of the first order and first degree.
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