A) \[1\]
B) \[2\]
C) \[3\]
D) None of these
Correct Answer: A
Solution :
Given equation is \[\sqrt{1+x}-a\sqrt{1+y}=1\] ?.(i) On differentiating w. r. t. x, we get \[\frac{1}{2\sqrt{1+x}}-\frac{a}{2+\sqrt{1+y}}.\frac{dy}{dx}=0\] \[\Rightarrow \] \[a=\frac{\sqrt{1+y}}{\sqrt{1+x}}.\frac{dx}{dy}\] On putting the value of a in Eq. (i), we get \[\sqrt{1+x}-\frac{\sqrt{1+y}}{\sqrt{1+x}}.\frac{dx}{dy}\times \sqrt{1+y}=1\] \[\Rightarrow \] \[(1+x)-(1+y).\frac{dx}{dy}=\sqrt{1+x}\] Hence, the degree is 1.
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