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 standard form of the equation of a circle with a center at \((h, k)\) and radius \(r\) is given by:

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

Given the center of the circle at \((0, 3)\) and a radius of \(3\), we can identify \(h = 0\), \(k = 3\), and \(r = 3\).

Now, substituting these values into the standard form, we get:

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

Simplifying this, we have:

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

Thus, filling in the missing information:

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

To summarize, the completed equation is:

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