+1206 Consider the circle defined by the equation \(x^2 +6x +y^2 +8y =0\). Find the sum of the coordinates of the center of the circle.
+36916 X^2 + 6x + y^2 + 8y = 0 'complete the square for 'x' and for 'y' variable
x^2 + 6x +9 +y^2 + 8y + 16 = 9 + 16
(x+3)^2 + ( y+4)^2 = 25 now the equation is of the form (x-h)^2 + (y-k)^2 = r^2
where (h,k) is the circle center.... (h,k) = (-3,-4)
sum is -3 + -4 = -7
+36916 X^2 + 6x + y^2 + 8y = 0 'complete the square for 'x' and for 'y' variable
x^2 + 6x +9 +y^2 + 8y + 16 = 9 + 16
(x+3)^2 + ( y+4)^2 = 25 now the equation is of the form (x-h)^2 + (y-k)^2 = r^2
where (h,k) is the circle center.... (h,k) = (-3,-4)
sum is -3 + -4 = -7
