+779 What is the area of the region defined by the equation $x^2+y^2 - 7 = 4y-14x+2x-6y+3$?
+37063 Re-arrange by simplifying to :
x^2 +12x +y^2 +2y = 10 Now complete the squares for x and y
x^2 + 12x +36 + Y^2 +2y +1 = 10 +36 + 1
(x+6)^2 + ( y+1)^2 = 47 47 is r^2 For this circle
Area of a circle = pi r^2 = pi * 47 = 47*pi = 147.65 units^2
