The equation of a circle in the Cartesian coordinate system can be written using the formula:
(x – h)² + (y – k)² = r²
In this formula:
- (h, k) is the center of the circle.
- r is the radius of the circle.
In your case, the center of the circle is given as (2, 3) and the radius is 3 units. Plugging these values into the formula, we have:
- h = 2
- k = 3
- r = 3
Substituting these values into the equation results in:
(x – 2)² + (y – 3)² = 3²
which simplifies to:
(x – 2)² + (y – 3)² = 9
So, the equation of the circle with center at (2, 3) and radius of 3 units is:
(x – 2)² + (y – 3)² = 9