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.(2 points)
(x−
)2+
(y−
)2=

Answer 1

The general equation of a circle with center \((h, k)\) and radius \(r\) is given by:

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

In your case, the center of the circle is at \((0, 3)\) and the radius is \(3\).

Here, you can identify:
- \(h = 0\)
- \(k = 3\)
- \(r = 3\)

Now, substitute these values into the equation:

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

This simplifies to:

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

So, filling in the missing information in your equation, we get:

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

In conclusion, with the missing information filled in, the equation becomes:

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

Therefore, the answers to fill in the blanks are:
- \(0\)
- \(3\)
- \(9\)