The graph of (x + 3)^2 + (y - 7)^2 = 16 is reflected over the line y = 2. The new graph is the graph of the equation x^2 + Bx + y^2 + Dy + F = 0 for some constants B, D, and F. Find B + D + F.
The center of the circle = ( -3, 7 )
When reflected across the line y = 2, the new center will be (-3, 2 - 5) = (-3,-3)
The new circle is
(x +3)^2 + ( y +3)^2 = 16
x^2 + 6x + 9 + y^2 + 6x + 9 =16
x^2 + 6x + y^2 + 6y + 2 = 0
B = 6 D = 6 F = 2
And their sum =14
