Question

question determine the equation of the circle graphed below. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Identify the center of the circle

From the graph, the center of the circle \((h,k)\) is at \((-3,0)\) (since it's 3 units to the left of the origin on the x - axis and 0 on the y - axis).

Step2: Determine the radius of the circle

The radius \(r\) is the distance from the center to a point on the circle. Looking at the graph, the distance from the center \((-3,0)\) to the origin \((0,0)\) (a point on the circle) is \(r = 3\) units.

Step3: Use the standard equation of a circle

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\). Substituting \(h=-3\), \(k = 0\) and \(r = 3\) into the equation:
\((x-(-3))^2+(y - 0)^2=3^2\)
Simplify the equation:
\((x + 3)^2+y^2=9\)

Answer:

\((x + 3)^2+y^2=9\)