A) \[y\text{ }\left[ 1+{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\]
B) \[y\text{ }\left[ 1-{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\]
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}+2\frac{dy}{dx}=0\]
D) \[{{\left( \frac{dy}{dx} \right)}^{3}}+3\,\frac{dy}{dx}+y=0\]
Correct Answer: B
Solution :
Given \[{{y}^{2}}=4a(x+a)\]. Differentiating, \[2y\,\left( \frac{dy}{dx} \right)=4a\] Eliminating a from (i) and (ii), required equation is \[y\text{ }\left[ 1-{{\left( \frac{dy}{dx} \right)}^{2}} \right]=2x\frac{dy}{dx}\].
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