Thread: Help with parametric equations?

Two particles move in the xy-plane. At time t, the position of particle A is given by x(t)=4t−4 and y(t)=2t−k, and the position of particle B is given by x(t)=3t and y(t)=t^2−2t−1.
Find k so that the particles are sure to collide.

My initial thought wast to take the derivatives of the equations, but then the k would just drop out, so that's not right.
Any suggestions? Thanks!

Originally Posted by iheartthemusic29

Two particles move in the xy-plane. At time t, the position of particle A is given by x(t)=4t−4 and y(t)=2t−k, and the position of particle B is given by x(t)=3t and y(t)=t^2−2t−1.
Find k so that the particles are sure to collide.

My initial thought wast to take the derivatives of the equations, but then the k would just drop out, so that's not right.
Any suggestions? Thanks!

If the two particles collide, then surely they have the same x and y values...


So and

From equation 1, .

So, when subbed into equation 2, we have

.

What is k?