Vector calculus for ellipse in polar coordinates

I'm having trouble with this question, can somebody please help me with it! I'll thanks/like your comment if help me =)
http://i.stack.imgur.com/YGKhm.png
I know that for a ellipse the parametric is x=a sin t , b= b cos t t:0 to 2pi (?)
for part a) I drew up the graph but not sure if it's right. the circle have 1 radius and for the ellipse I able to find the x= 2 (x-1)^2 =9
sqrt(x-1)^2=sqrt9 x-1=3 x=4
for y=2sqrt2 y^2=8 sqrty=sqrt8 y=sqrt4 sqrt 2 y= 2sqrt2 or 2.8
So the region should be the circle? since the ellipse like cover the whole circle? Thank you very much for helping! Cheers.

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

Attachment 28425

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 $\displaystyle 0 \leq t<2 \pi $ 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.