The standard form of the equation of a circle is given by the formula:
(x – h)² + (y – k)² = r²
where (h, k) is the center of the circle and r is the radius.
In this case, the center of the circle is at (2, 5), so h = 2 and k = 5. The radius is given as 4 units, which means r = 4.
Substituting these values into the formula, we get:
(x – 2)² + (y – 5)² = 4²
Now, calculating 4² gives us 16, so the equation simplifies to:
(x – 2)² + (y – 5)² = 16
This is the equation of the circle with a center at (2, 5) and a radius of 4 units.