What is the area of the portion of the circle defined by \(x^2-12x+y^2=28\) that lies above the \(x\)-axis and to the right of the line \(y=6-x\)?
This is a circle centered at 6,0 with aradius of 8
The line goes right through the center ...and has a slope of -1
so it forms a 135o angle with the x axis
Total area = pi 8^2
for the 135 degree portion 135/360 * pi * 82 = 75.4 units2
Here is a picture: