Question

1. which equation is correct for the circle shown on the graph below? (x - 3)^2+(y - 0)^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 center and radius from the graph

By observing the graph, assume the center of the circle is $(h,k)$ and the radius is $r$. If we can count the grid - squares, we can determine these values. Let's assume the center of the circle is at a point such that by counting the horizontal and vertical distances from the origin. If the center of the circle is at $(h,k)$ and we count the number of units from the center to a point on the circle to get the radius $r$.

Step3: Substitute values into the formula

If the center of the circle is $(h,k)$ and radius $r$, then the equation of the circle is $(x - h)^2+(y - k)^2=r^2$. For example, if the center is $(3,6)$ and radius $r = 2$, the equation is $(x - 3)^2+(y - 6)^2=4$.

Since the equation $(x - 3)^2+(y - 6)^2=4$ is given at the bottom of the picture (assuming the center is $(3,6)$ and radius $r = 2$), we can analyze it based on the standard form. The general form of a circle equation $(x - h)^2+(y - k)^2=r^2$ has $(h,k)$ as the center and $r$ the radius. Here $h = 3,k = 6,r=2$ (because $r^2 = 4$ implies $r = 2$).

Answer:

If the center of the circle is $(3,6)$ and radius $r = 2$, the correct equation for the circle is $(x - 3)^2+(y - 6)^2=4$