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A particle is moving with a velocity v = K(yî + xĵ), where K is a constant. The general equation for its path is:

1. y = x² + constant
2. y² = x + constant
3. y² = x² + constant
4. xy = constant

Correct answer: y² = x² + constant

Solution

The correct option describes a relationship between x and y that arises from the particle's velocity components, which are proportional to each other. By integrating the velocity components, we find that the path of the particle follows a quadratic relationship, specifically in the form of a circle or parabola, leading to the equation y² = x² + constant.

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