Curve of a particle

Problem

A particle moves along $x(t)=t$, $y(t)=t^2$. What curve does it trace? In implicit form?

Solution

Since $x=t$, substituting $t=x$ into the second equation eliminates the parameter: $y = t^2 = x^2.$ The curve is the parabola $\boxed{y=x^2}$, in implicit form $y-x^2=0$.

Links

Topics: Complex numbers
Concepts: Implicit form · Parametrisation
Skills: Modelling
Exercise type: Modelling problem