Dragonxhell,

They say that the region is between the two curves, you are thinking about the intersection when you say that the region is the circle, let me send you a graph to show you what I mean

Another thing, the parametrization you wrote is for an ellipse centered at (0,0), this one is centered at (1,0).

The general form of an ellipse with parametrization t, with is x= a*cos(t) + h and y = b*sin(t) +k. Where (h,k) is the center of the ellipse.

The red area is the region in question. Try to pick it up from there and feel free to ask again if you get stuck.

Regards,

Damián Vallejo

You can visit my blog if you want, it is Math 911 I discuss various math topics there.