The equation of a circle in the Cartesian coordinate system can be formulated using the standard equation:
(x – h)² + (y – k)² = r²
In this equation, (h, k) represents the center of the circle and r represents the radius.
Given the center (3, 2) and radius 5, we can substitute these values into the standard form:
- h = 3
- k = 2
- r = 5
Now, substituting these into the equation:
(x – 3)² + (y – 2)² = 5²
Calculating 5² gives us 25, so the equation becomes:
(x – 3)² + (y – 2)² = 25
This is the equation of the circle centered at (3, 2) with a radius of 5.