A) \[{{y}^{2}}={{x}^{2}}+constant\]
B) \[y={{x}^{2}}+constant\]
C) \[{{y}^{2}}=x+constant\]
D) \[xy=constant\]
Correct Answer: A
Solution :
\[\overrightarrow{v}=ky\hat{i}+kx\hat{j}\] \[\Rightarrow \] \[\frac{dx}{dt}=ky,\frac{ky}{dt}=kx\] \[\therefore \]\[\frac{dy}{dx}=\frac{x}{y}\]\[\Rightarrow \]\[\int{ydy}=\int{x}\,dx\] \[\]
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