find the area between two concentric circles defined by x 2 + y 2 - 2 x + 4 y + 1 = 0 x 2 + y 2 - 2 x + 4 y - 11 = 0
rewrite equations of circles in standard form . hence equation x 2 + y 2 - 2 x + 4 y + 1 = 0 may be written as ( x - 1 ) 2 + ( y + 2 ) 2 = 4 = 22 and equation x 2 + y 2 - 2 x + 4 y - 11 = 0 as ( x - 1 ) 2 + ( y + 2 ) 2 = 16 = 42 knowing the radii , the area of the ring is pi ( 4 ) 2 - pi ( 2 ) 2 = 12 pi correct answer is b ) 12 pi
multiply(add(divide(add(11, const_3), const_100), const_3), subtract(add(add(power(divide(4, 2), const_2), divide(2, 2)), 11), subtract(add(power(divide(4, 2), const_2), divide(2, 2)), 1)))