Question

The figure below shows the ellipse $\frac{(x-20)^2}{20}+\frac{(y-16)^2}{16}=2016$.
[asy]
defaultpen(linewidth(0.7));
pair c=(20,16);
real dist = 30;
real a = sqrt(2016*20),b=sqrt(2016*16);
xaxis("x",c.x-a-dist,c.x+a+3*dist,EndArrow);
yaxis("y",c.y-b-dist*2,c.y+b+3*dist,EndArrow);
draw(ellipse(c,a,b));
label("$R_1$",(100,100));
label("$R_2$",(-80,100));
label("$R_3$",(-60,-75));
label("$R_4$",(70,-75));
[/asy]
Let $R_1,R_2,R_3,$ and $R_4$ denote those areas within the ellipse that are in the first, second, third, and fourth quadrants, respectively. Determine the value of $R_1-R_2+R_3-R_4$.

Answer 1

1280