<----- a=1, b increases
We see that as b increases, our circle seems to be smushed into an ellipse. It is very interesting that it seems to be stretched out more the higher b becomes. If we think about these curves in terms of their coordinates, the x-coordinate will always be just cos(t) like on our unit circle. But as we increase b, our y-coordinate increases, causing the orginal unit circle to stretch out.
|In this illustration, b is held constant at two while a increases. We see the same thing happening now that we did before, except for now the y-coordinate stays the same wile the x-coordinate stretches out. Think about this in the same way that we though about the unit circle.|