The solution set of an equation of a circle is all of the points that lie in the circle.

The solution set of an equation of a circle is indeed comprised of all the points that lie within the circle, including the boundary.

In general, the equation of a circle in the Cartesian coordinate plane can be expressed as:

$(x - h)^2 + (y - k)^2 = r^2$

where:

• $(h, k)$ represents the coordinates of the center of the circle.
• $r$ is the radius of the circle.

1. Understanding the Equation: The left side, $(x - h)^2 + (y - k)^2$, represents the distance from any point $(x, y)$ to the center of the circle $(h, k)$. The equation states that this distance is equal to $r$, the radius.

2. Solution Set: The solution set includes all points $(x, y)$ that satisfy this equation. Thus, it encompasses every point inside the circle as well as the points on the circle itself (where the distance equals $r$).

3. Graphical Representation: Visually, if you were to graph the circle defined by the equation, the solution set would include all points that are filled within the circular boundary along with the boundary itself.

In summary, for any given circle defined by its center and radius, the solution set consists of every point internally and on the circumference of the circle, providing a complete representation of its area.