Question

A circle is drawn on a coordinate plane with the center point at (0,3) and a radius of 3. Derive the equation of the circle from the given information. Fill in the missing information in the following equation.

(x - __)^2 + (y - __)^2 = ___

Answer 1

To derive the equation of a circle from the provided information, we use the standard form of the equation of a circle, which is:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

where \((h, k)\) is the center of the circle and \(r\) is the radius.

Given:

- Center point: \((0, 3)\)
- Radius: \(3\)

From this, we can identify:

- \(h = 0\)
- \(k = 3\)
- \(r = 3\)

Now, we can calculate \(r^2\):

\[
r^2 = 3^2 = 9
\]

Now we can fill in the missing information in the equation:

\[
(x - 0)^2 + (y - 3)^2 = 9
\]

So, the filled equation is:

\[
(x - 0)^2 + (y - 3)^2 = 9
\]

To summarize, the missing information is:

- First blank: \(0\)
- Second blank: \(3\)
- Third blank: \(9\)

Thus, the complete equation of the circle is:

\[
(x - 0)^2 + (y - 3)^2 = 9
\]