The general equation of a circle in the Cartesian coordinate system can be expressed as:
(x – h)² + (y – k)² = r²
In this equation:
- (h, k) is the center of the circle.
- r is the radius.
Given that the center of the circle is at the point (2, 1) and the radius is 3, we can substitute these values into the general equation:
- h = 2
- k = 1
- r = 3
Substituting these values into the circle equation:
(x – 2)² + (y – 1)² = 3²
Calculating the square of the radius:
3² = 9
Therefore, the equation becomes:
(x – 2)² + (y – 1)² = 9
This is the equation of the circle whose center is at the point (2, 1) and has a radius of 3. It describes all the points (x, y) that are exactly 3 units away from the center (2, 1) in the Cartesian plane.