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 = 2

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 of the circle

From the graph, the center of the circle is at the point $(0,- 3)$, so $h = 0$ and $k=-3$.

Step3: Determine the radius of the circle

The radius $r$ is the distance from the center $(0,-3)$ to a point on the circle. By counting the grid - squares, we find that $r = 2$.

Step4: 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:

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