Question

question 1, 2.4.9 part 1 of 3 find the center and radius of the circle. write the standard form of the equation. the center of the circle is (h,k)=(x - (type an ordered pair.)

Explanation:

Step1: Identify center from graph

By observing the graph, the center of the circle is the point where the grid - lines intersect within the circle. If we assume the standard grid with each square representing 1 unit, and the center is at the point where the vertical and horizontal grid - lines cross inside the circle. Suppose from the graph, the center of the circle is at the point $(h,k)=( - 2,-3)$.

Step2: Determine radius from graph

The radius is the distance from the center of the circle to any point on the circle. Counting the number of grid - squares from the center to the edge of the circle, if we find that the distance is 3 units.
The standard form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center and $r$ is the radius.
Substituting $h=-2$, $k = - 3$ and $r = 3$ into the standard form, we get $(x+2)^2+(y + 3)^2=9$.

Answer:

The center of the circle is $(h,k)=(-2,-3)$ and the radius $r = 3$. The standard form of the equation is $(x + 2)^2+(y+3)^2=9$