Question

writing an equation given a graph. what is the equation of the circle shown in the graph? (x - 3)^2+y^2 = 4; (x + 3)^2+y^2 = 2; x^2+(y + 3)^2 = 4; x^2+(y - 3)^2 = 4

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify the center and radius from the graph

From the graph, the center of the circle is $(0, - 3)$ and the radius $r = 2$.

Step3: Substitute values into the formula

Substitute $h = 0$, $k=-3$, and $r = 2$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-0)^2+(y + 3)^2=2^2$, which simplifies to $x^{2}+(y + 3)^{2}=4$.

Answer:

$x^{2}+(y + 3)^{2}=4$