The position vector of a particle is **r** = (t^{2}-1)**i** + 2t**j**. Determine the trajectory of the particle in the 'xy ' plane.

the standard form of the position vector is given as

**r **= **i**x +** j**y

so,

by comparing it with the given equation

r = (t^{2} - 1)**i** + 2t**j**

we get

x = t^{2} - 1

y = 2t or t = y/2

thus, we get

x = (y/2)^{2} - 1

thus, the equation of trajectory will be

**x = (y**^{2}**/4) - 1**

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