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  4. A particle is moving with a velocity vecv = K (y hati + x hatj) , where K is a constant. The general equation for its path is:

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Q. A particle is moving with a velocity $\vec{v} = K (y \hat{i} + x \hat{j})$ , where $K$ is a constant. The general equation for its path is:

JEE MainJEE Main 2019Motion in a Plane

Solution:

$\frac{dx}{dt} = ky, \frac{dy}{dt} =kx $
Now, $\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{x}{y} $
$ \Rightarrow ydy = xdx $
Integrating both side
$y^{2} = x^{2} +c $