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 coordinates

From the graph, the center of the circle is at \((-6, 5)\) (by observing the grid, the center is 6 units left of the origin on the x - axis and 5 units up on the y - axis).

Step3: Determine the radius

By counting the grid units from the center to the edge of the circle, the radius \(r = 2\) (since the distance from the center to the top, bottom, left, or right of the circle is 2 units).

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

Substitute \(h=-6\), \(k = 5\), and \(r = 2\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x-(-6))^2+(y - 5)^2=2^2\), which simplifies to \((x + 6)^2+(y - 5)^2=4\).

Answer:

\((x + 6)^2+(y - 5)^2 = 4\)