Find the equation for the following circle:

$x^2+y^2=4$

$$\left$(x+1$\right$)^2+y^2=4$

$$\left$(x-1$\right$)^2+y^2=4$

$$\left$(x+1$\right$)^2+y^2=16$

Verified step by step guidance

Step 1: Identify the center of the circle from the graph. The center is located at (-1, 0), as indicated by the red dot in the graph.

Step 2: Determine the radius of the circle. Measure the distance from the center (-1, 0) to any point on the circle's edge. For example, the radius extends to (-1, 2) or (-1, -2), giving a radius of 2 units.

Step 3: Recall the general equation of a circle:

(^{x - h) 2} + (^{y - k) 2} = r^{2}

, where (h, k) is the center and r is the radius.

Step 4: Substitute the center (-1, 0) and radius 2 into the equation. This gives:

(^{x + 1) 2} + y^{2} = 4

Step 5: Verify the equation by checking that points on the circle satisfy it. For example, substitute (1, 0) or (-1, 2) into the equation to confirm correctness.

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