JEE Main & Advanced Physics Two Dimensional Motion JEE PYQ - Two Dimensional Relative Motion

A particle is moving with velocity) \[\overrightarrow{v}=K(y\hat{i}+x\hat{j})\]where K is a constant. The general equation for its path is [AIEEE 2010]

A) (a)\[{{y}^{2}}={{x}^{2}}+constant\]

B) \[y={{x}^{2}}+constant\]

C) \[{{y}^{2}}=x+constant\]

D) \[xy=constant\]

Correct Answer: A

Solution :

[a] \[\overrightarrow{v}=ky\hat{i}+kx\hat{j}\]

\[\Rightarrow \] \[\frac{dx}{dt}=ky,\frac{ky}{dt}=kx\]

\[\therefore \]\[\frac{dy}{dx}=\frac{x}{y}\]\[\Rightarrow \]\[\int{ydy}=\int{x}\,dx\]

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