The coordinates of a particle moving in the X | vedclass

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(C) Given the coordinates of the particle as functions of time $t$:$x = 4t^2$$y = 2t$To find the locus (path) of the particle,we eliminate the paramet

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Parabola

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(C) Given the coordinates of the particle as functions of time $t$:$x = 4t^2$$y = 2t$To find the locus (path) of the particle,we eliminate the parameter $t$ from the equations.From the second equation,we have $t = \frac{y}{2}$.Substituting this value of $t$ into the first equation:$x = 4 \left( \frac{y}{2} \right)^2$$x = 4 \left( \frac{y^2}{4} \right)$$x = y^2$The equation $x = y^2$ represents a parabola opening along the positive $x$-axis.Therefore,the locus of the particle is a parabola.

The coordinates of a particle moving in the $XY$-plane vary with time as $x = 4t^2$ and $y = 2t$. The locus of the particle is a:

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