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)

Question

(x−
)2+(y−
)2=

Answer 1

The standard form of the 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 \((0, 3)\), which means \(h = 0\) and \(k = 3\). The radius \(r\) is 3, so \(r^2 = 3^2 = 9\).

Now, substituting the values into the equation:

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

This simplifies to:

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

Thus, filling in the missing information for the equation:

(x− 0 )² + (y− 3 )² = 9