why parametric coordinates are called as silent curve
Each value of t defines a point that we can plot. The collection of points that we get by letting t be all possible values is the graph of the parametric equations and is called the parametric curve. To help visualize just what a parametric curve is pretend that we have a big tank of water that is in constant motion and we drop a ping pong ball into the tank. The point will then represent the location of the ping pong ball in the tank at time t and the parametric curve will be a trace of all the locations of the ping pong ball. Note that this is not always a correct analogy but it is useful initially to help visualize just what a parametric curve is.