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

The standard equation of a circle in the coordinate plane is given by

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

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

From the information provided, the center of the circle is \((0, 3)\), which means \(h = 0\) and \(k = 3\). The radius is given as \(3\), so \(r = 3\).

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

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

Now we can fill in the blanks in the equation:

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

Thus, the filled equation is:

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

So, the missing information is:

- First blank (h): **0**
- Second blank (k): **3**
- Third blank (r²): **9**