The equation of a circle can be derived from its center coordinates and radius. In general, the standard form of the equation of a circle is given by:
(x - h)2 + (y - k)2 = r2
Here, (h, k) represents the coordinates of the center of the circle, and r represents the radius. Given that the center of the circle is at (2, 5) and the radius is 12, we can substitute these values into the equation:
- h = 2
- k = 5
- r = 12
Now, plugging these values into the standard form:
(x - 2)2 + (y - 5)2 = 122
Calculating the square of the radius:
122 = 144
Therefore, the equation of the circle becomes:
(x - 2)2 + (y - 5)2 = 144
This equation represents all the points (x, y) that are at a distance of 12 units from the center (2, 5).