A) \[{{\left( \frac{dy}{dx} \right)}^{2}}=2y\frac{dy}{dx}\]
B) \[{{\left( \frac{dy}{dx} \right)}^{2}}-2y\frac{dy}{dx}+1=0\]
C) \[2y{{\left( \frac{dy}{dx} \right)}^{2}}+1=0\]
D) \[{{\left( \frac{dy}{dx} \right)}^{2}}+2y\frac{dy}{dx}+1=0\]
Correct Answer: B
Solution :
[b] Area \[=\frac{1}{2}(ST+SN)\times PS\] \[\Rightarrow \,\,\,\,{{y}^{3}}=\frac{1}{2}\left( yy'+\frac{y}{y'} \right)y\] (Given) \[\Rightarrow \,\,\,\,2y=y'+\frac{1}{y'}\] \[\Rightarrow \,\,\,\,{{\left( \frac{dy}{dx} \right)}^{2}}-2y\left( \frac{dy}{dx} \right)+1=0\]You need to login to perform this action.
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