A circle is described by the equation x2−10x+y2+8y=6
. Identify the center and radius of the circle.

x² - 10x + y² + 8y = 6

x² + y² - 10x + 8y - 6 = 0

Center = (-(1/2)A, -(1/2)B)

= (-(1/2)(-10), -(1/2)(8))

= (5, -4)

Radius = √((1/4)A² + (1/4)B² - C)

= √((1/4)(-10)² + (1/4)8² - (-6))

= √((1/4)(100) + (1/4)(64) + 6)

= √(25 + 16 + 6)

= √47

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2