The equation of a circle is generally 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 the point (4, 9). The diameter of the circle is 10 units, which means the radius is half of that, so:
r = diameter / 2 = 10 / 2 = 5
Now, we can substitute the values of h, k, and r into the circle equation:
(x – 4)² + (y – 9)² = 5²
Calculating 5² gives us 25, so we have:
(x – 4)² + (y – 9)² = 25
Therefore, the equation that represents the circle with center (4, 9) and diameter of 10 units is:
(x – 4)² + (y – 9)² = 25