[tex]x^2+(y+2)^2=8^2[/tex]
Explanation:
We apply the equation of circle instandard form:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{where the center of circle = (h, k)} \\ r\text{ = radius} \end{gathered}[/tex]
We need to determine the center of circle from the graph given:
From the graph, the center is at 2 units below the origin (0, 0) on the y axis.
This coordinate corresponds to (0, -2)
The center (h, k) = (0, -2)
h = 0 and k = -2
The radius is the distance from the center of the circle to the circumference.
The distance is 8 units
radius = 8 units
Inserting the formula into the equation:
[tex]\begin{gathered} (x-0)^2+(y-(-2))^2=8^2 \\ x^2+(y+2)^2=8^2\text{ or} \\ x^2+(y+2)^2=\text{ 64} \end{gathered}[/tex]
