This is probably a simple question but:

r(t) is the position of a particle in the xy-plane at time t.Find an equation in x and y whose graph is the path of the particle.Then find the particle's velocity and acceleration vectors at the given time t.

Ok, I know how to find the velocity and acceleration vectors at the given time, but I'm not sure how to do the part in bold. The answer given in the book is but I don't understand they arrived at that. Any help would be appreciated. Thanks