Question

what is the standard form of the equation of the circle shown below? a $(x - 2)^2+(y - 2)^2 = 16$ b $(x + 2)^2+(y - 2)^2 = 16$ c $(x - 2)^2+(y + 2)^2 = 16$ d $(x + 2)^2+(y + 2)^2 = 16$

Explanation:

Step1: Recall the standard form of a circle equation

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

Step2: Determine the center of the circle

From the graph, the center of the circle is \((- 2,2)\). So \(h=-2\) and \(k = 2\). Substituting into the standard form gives \((x-(-2))^2+(y - 2)^2=r^2\), which simplifies to \((x + 2)^2+(y - 2)^2=r^2\).

Step3: Determine the radius of the circle

By counting the grid - points (or using the distance formula from the center to a point on the circle), the radius \(r = 4\). Then \(r^2=16\).

Answer:

B. \((x + 2)^2+(y - 2)^2=16\)