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Question Number 59936 by Sardor2211 last updated on 16/May/19

Answered by tanmay last updated on 16/May/19

$$x\sqrt{1+y^2}+\frac{dy}{dx}.y.\sqrt{1+x^2}=0$$$$x\sqrt{1+y^2}dx+y\sqrt{1+x^2}dy=0$$$$\frac{xdx}{\sqrt{1+x^2}}+\frac{ydy}{\sqrt{1+y^2}}=dc$$$$\frac{1}{2}\int \frac{d(1+x^2)}{\sqrt{1+x^2}}+\frac{1}{2}\int \frac{d(1+y^2)}{\sqrt{1+y^2}}=\int dc$$$$\frac{\sqrt{1+x^2}}{\frac{1}{2}}\times \frac{1}{2}+\frac{\sqrt{1+y^2}}{\frac{1}{2}}\times \frac{1}{2}=c$$$$\sqrt{1+x^2}+\sqrt{1+y^2}=c$$

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