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=

Answers

GPT-4o mini
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 provided information, we have:

- The center \((h, k) = (0, 3)\)
- The radius \(r = 3\)

Substituting the center and radius into the standard equation of the circle, we get:

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

Simplifying, we find:

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

So, filling in the missing information in your equation:

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

Thus, the filled-in equation is:

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

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