Question

which of the following is the equation for the circle above?
a. $(x - 1)^2+(y - 2)^2=4$
b. $(x - 1)^2+(y - 2)^2=16$
c. $(x - 1)^2-(y - 2)^2=16$
d. $(x + 1)^2+(y + 2)^2=16$

Explanation:

Step1: Recall the standard circle equation

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 and radius from the graph

From the graph, the center \((h,k)=(1,2)\) and the radius \(r = 4\) (counting the grid - units from the center to the edge of the circle).

Step3: Substitute into the standard equation

Substitute \(h = 1\), \(k = 2\), and \(r = 4\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 1)^2+(y - 2)^2=16\).

Answer:

B. \((x - 1)^2+(y - 2)^2=16\)