Which term describes the set of all points at a fixed distance from a given center?

Which term describes the set of all points at a fixed distance from a given center?

• A. Ellipse
• B. Parabola
• C. Circle
• D. Polygon

Answer: (C)

The main idea is that the locus of all points at a fixed distance from a center forms a circle. If you fix a center and a distance r, every point exactly r units away from that center lies on the boundary of a round shape, and tracing all those points around the center creates a circle. The radius is that fixed distance r. The other shapes come from different definitions: an ellipse comes from points where the sum of distances to two fixed points is constant; a parabola comes from points equidistant from a fixed point (focus) and a fixed line (directrix); a polygon is a closed figure made of straight-line segments. So the term for the described set is circle.

The main idea is that the locus of all points at a fixed distance from a center forms a circle. If you fix a center and a distance r, every point exactly r units away from that center lies on the boundary of a round shape, and tracing all those points around the center creates a circle. The radius is that fixed distance r. The other shapes come from different definitions: an ellipse comes from points where the sum of distances to two fixed points is constant; a parabola comes from points equidistant from a fixed point (focus) and a fixed line (directrix); a polygon is a closed figure made of straight-line segments. So the term for the described set is circle.