Sure, let's solve this problem step by step.
1. Identify the center of the circle:
The problem statement tells us that the circle is centered at the origin. The origin in a Cartesian coordinate system is the point [tex]\((0, 0)\)[/tex]. So, the center of the circle is:
[tex]\[
\text{Center} = (0, 0)
\][/tex]
2. Determine the radius:
The radius of the circle is given as [tex]\(3 \sqrt{2}\)[/tex] units. This is a straightforward representation and does not require any further manipulation to understand. However, for the sake of completeness, if we were to express [tex]\(3 \sqrt{2}\)[/tex] in decimal form, it would approximate to:
[tex]\[
3 \sqrt{2} \approx 4.242640687119286
\][/tex]
3. Compile the information:
- Center of the circle: [tex]\((0, 0)\)[/tex]
- Radius of the circle: [tex]\(4.242640687119286\)[/tex] units
So, the detailed properties of the circle are:
- The center is at [tex]\((0, 0)\)[/tex].
- The radius is approximately [tex]\(4.242640687119286\)[/tex] units.
Therefore, the solution for the given problem is:
[tex]\[
((0, 0), 4.242640687119286)
\][/tex]
