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 equation of a circle in the coordinate plane can be expressed using the formula:

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

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

From the information given:
- The center of the circle is \((0, 3)\), so \(h = 0\) and \(k = 3\).
- The radius is \(3\), so \(r = 3\).

Now, substituting these values into the equation:

1. \(h = 0\)
2. \(k = 3\)
3. \(r^2 = 3^2 = 9\)

Putting it all together in the equation:

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

So, filling in the missing information:

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

Thus, the finalized equation is:

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