The equation x² + y² = 4 represents a circle centered at the origin (0, 0) with a radius of 2. This is derived from the general form of a circle’s equation, which is (x – h)² + (y – k)² = r², where (h, k) is the center and r is the radius. In this case, since there are no (h, k) terms added to x or y, the center is at (0, 0), and the right side of the equation, 4, indicates that the radius squared (r²) is equal to 4, thus the radius (r) is 2.
Now, referring to the inequality x² + y² < 4, this describes all points (x, y) that are inside the circle. Specifically, any point that satisfies this inequality will have a distance from the center that is less than the radius of the circle. Conversely, the inequality x² + y² > 4 would represent points outside the circle.
Therefore, the solution set to the inequality x² + y² < 4 indicates all points that lie within the circle with radius 2 centered at the origin.