Question

what is the equation of the given circle?
a. $(x + 3)^{2}+(y - 2)^{2}=1$
b. $(x - 3)^{2}+(y + 2)^{2}=1$
c. $(x + 3)^{2}+(y - 2)^{2}=2$
d. $(x - 3)^{2}+(y + 2)^{2}=2$

Explanation:

Step1: Recall the standard form of a circle's equation

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

Step2: Determine the center of the circle

From the graph, the center of the circle \((h,k)=(- 3,2)\). So \(h=-3\) and \(k = 2\). Substituting into the standard form, we get \((x-(-3))^2+(y - 2)^2=r^2\), which simplifies to \((x + 3)^2+(y - 2)^2=r^2\).

Step3: Determine the radius of the circle

By observing the graph, the radius \(r = 1\) (since the distance from the center to a point on the circle is 1 unit). Then \(r^2=1\).

Answer:

A. \((x + 3)^2+(y - 2)^2=1\)