Find the equation for the following circle:

• A. $x^2+y^2=4$
• B. $\left(x+1\right)^2+y^2=4$
• C. $\left(x-1\right)^2+y^2=4$
• D. $\left(x+1\right)^2+y^2=16$

Answer: (D)

Verified step by step guidance

1. Identify the center of the circle from the graph. The center is at (-1, 0).
2. Determine the radius of the circle by measuring the distance from the center to any point on the circle. The radius is 4 units.
3. Recall the standard form of a circle's equation: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.
4. Substitute the center (-1, 0) and the radius 4 into the standard form equation: (x + 1)^2 + (y - 0)^2 = 4^2.
5. Simplify the equation to get the final form: (x + 1)^2 + y^2 = 16.