The position vector of a particle is r = (t²-1)i + 2tj. Determine the trajectory of the particle in the 'xy ' plane.

the standard form of the position vector is given as

r = ix + jy

so, 

by comparing it with the given equation

r = (t² - 1)i + 2tj

we get

x = t² - 1

y = 2t or t = y/2

thus, we get

x = (y/2)² - 1

thus, the equation of trajectory will be

x = (y²/4) - 1