Question

determine the equation of the circle graphed below.

Explanation:

Step1: Recall the circle equation formula

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step2: Identify the center of the circle

From the graph, the center of the circle is at \((-3, -7)\) (by looking at the grid, the center is 3 units left of the origin on the x - axis and 7 units down on the y - axis).

Step3: Determine the radius of the circle

By counting the grid units from the center to the edge of the circle, we can see that the radius \(r = 2\) (the distance from the center \((-3,-7)\) to a point on the circle, like \((-3,-5)\) or \((-1,-7)\) or \((-5,-7)\) is 2 units).

Step4: Substitute \(h\), \(k\), and \(r\) into the circle equation

Substitute \(h=-3\), \(k = -7\), and \(r = 2\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - (-3))^2+(y - (-7))^2=2^2\), which simplifies to \((x + 3)^2+(y + 7)^2 = 4\).

Answer:

\((x + 3)^2+(y + 7)^2 = 4\)