Question

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

A
xy=constant
B
y2=x2+constant
C
y=x2+constant
D
y2=x+constant

Solution

## The correct option is B $$y^2 = x^2+constant$$$$\dfrac{dx}{dt} = ky, \, \dfrac{dy}{dt} = kx$$Now, $$\dfrac{dy}{dx} = \dfrac{\dfrac{dy}{dt}}{\dfrac{dx}{dt}} = \dfrac{x}{y}$$$$\Rightarrow ydy = xdx$$Integrating both side$$y^2 = x^2 + c$$Physics

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