Final answer:
The equation of the circle with center (-2,0) and an area of 49π is (x+2)² + y² = 49.
Step-by-step explanation:
The equation of a circle in the xy-plane with a given center and area can be found using the formula (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.
The area of the circle is given by A = πr². If the area is 49π, then r² = 49. Therefore, r = 7. Substituting the center (-2,0) and r = 7 into the circle's equation, we get (x+2)² + y² = 49.