Question

Describe the similarities and the differences between the graphs of (x + 3)^2 + (y - 4)^2 = 16 and (x - 3)^2 + (y - 2)^2 = 16.

Answer 1

\[\left( x - a \right)^2 + \left( y - b \right)^2 = r^2\] This is a graph of a circle with radius r and center (a,b)

Answer 2

(x + 3)^2 + (y - 4)^2 = 16 can be rewritten as
(x - (- 3))^2 + (y - 4)^2 = 4^2 so this is the equation of a
circle centered at (-3,4) with radius 4
Similarly (x - 3)^2 + (y - 2)^2 = 16 can be rewritten as
(x - 3)^2 + (y - 2)^2 = 4^2 which is the equation of the circle centered at
(3,2) with radius 4.