Final Answer:
The center of the circle is at (7, 2), and its radius is 5 units.
Step-by-step explanation:
To determine the center and radius of the circle represented by the equation (x-7)² + (y-2)² = 25, we recognize that the equation is in the standard form of the circle's equation: (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r is the radius.
Comparing the given equation to the standard form, we can identify that the center of the circle is at (h, k) = (7, 2). This implies that the x-coordinate of the center is 7, and the y-coordinate is 2. Therefore, the center of the circle is at point (7, 2).
Moreover, the radius of the circle (r) is given by the square root of the constant value on the right side of the equation. In this case, the constant is 25. Taking the square root of 25, we get the radius, which is 5 units. Hence, the circle's radius is 5 units.
In conclusion, the equation (x-7)² + (y-2)² = 25 represents a circle with its center at (7, 2) and a radius of 5 units. This information enables us to graph the circle accurately on a coordinate plane or use it for further calculations involving the circle's properties and interactions with other geometric figures.