You are integrating this: 2\pi \int_{0}^{\frac{\pi }{2}} x(1-sinx)dx
Type this in http://www.codecogs.com/latex/eqneditor.php to make it easier to read. For some reason I can't post latex.
It says the focal chord is perpendicular to the axis, therefore you are looking at the area between y=0 and y=a. So just integrate x=(4ay)^0.5 in that limit, I think you should get the area.
Carrot, why you no free up some space to tutor me some harder MX2 :( hope Sean has some space, need a good MX2 tutor asap, looks like I'll not get one :'(