Question

write the equation of this circle in standard form.

Explanation:

Step1: Identify the center of the circle

Looking at the graph, the center of the circle is at the point \((-8, -9)\) (by counting the grid units: 8 units left on the x - axis and 9 units down on the y - axis).

Step2: Determine the radius of the circle

From the graph, we can see that the radius \(r = 1\) (since the circle spans 1 unit from the center to the edge).

Step3: Use the standard form of the circle's equation

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius. Substituting \(h=-8\), \(k = - 9\) and \(r = 1\) into the formula, we get \((x-(-8))^2+(y - (-9))^2=1^2\), which simplifies to \((x + 8)^2+(y+9)^2 = 1\).

Answer:

\((x + 8)^2+(y + 9)^2=1\)