
< 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 xcoordinate will always be just cos(t) like on our unit circle. But as we increase b, our ycoordinate 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 ycoordinate stays the same wile the xcoordinate stretches out. Think about this in the same way that we though about the unit circle. 