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 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:

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