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=
(x−
)2+(y−
)2=
Answers
GPT-4o mini
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**
\[
(x - h)^2 + (y - k)^2 = r^2
\]
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**