A) \[{{x}^{2/3}}-{{y}^{2/3}}=c\]
B) \[{{x}^{4/3}}-{{y}^{4/3}}=c\]
C) \[{{x}^{4/3}}+{{y}^{4/3}}=c\]
D) \[{{x}^{1/3}}-{{y}^{1/3}}=c\]
Correct Answer: B
Solution :
[b] \[{{x}^{2/3}}+{{y}^{2/3}}={{a}^{2/3}}\] Or \[\frac{2}{3}{{x}^{-1/3}}+\frac{2}{3}{{y}^{-1/3}}\frac{dy}{dx}=0\] Or \[\frac{dy}{dx}=-\frac{{{x}^{-1/3}}}{{{y}^{-1/3}}}\] ...(1) Replacing \[\frac{dy}{dx}\left( \frac{\pi }{2}-\theta \right)\]by\[-\frac{dx}{dy}\], we get \[\frac{dx}{dy}=\frac{{{x}^{-1/3}}}{{{y}^{-1/3}}}\] Or \[\int{{{x}^{1/3}}dx=\int{{{y}^{1/3}}dy}}\] Or \[{{x}^{4/3}}-{{y}^{4/3}}=c\]
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