What is a key component of the equation (x-a)² + (y-b)² = r²?

The equation ((x-a)² + (y-b)² = r²) describes a circle in a Cartesian coordinate system. In this equation, ((a, b)) represents the coordinates of the center of the circle, while (r) is the radius.

The equation can be understood as follows: it states that any point ((x, y)) on the circle is at a distance (r) (the radius) from the center point ((a, b)). The terms (x-a) and (y-b) measure the horizontal and vertical distances from the center to any point on the circle. When squared and added together, they equal the square of the radius, which is a fundamental property of circles.

Thus, the center of the circle is indeed a key component of the given equation, as it establishes the exact location from which all points on the circle are equidistant by the radius (r). This makes option A the correct choice, as it directly relates to the core characteristics of the circle defined by the equation.