The equation of a circle in a Cartesian coordinate system can be defined using the standard formula:
(x – h)² + (y – k)² = r²
In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius.
In your case, the center of the circle is at the point (1, 2). Therefore, h = 1 and k = 2. The radius of the circle is 3 units, meaning r = 3.
Now, substituting the values into the standard formula:
(x – 1)² + (y – 2)² = 3²
This simplifies to:
(x – 1)² + (y – 2)² = 9
So, the equation of the circle with center (1, 2) and radius 3 is:
(x – 1)² + (y – 2)² = 9