Which concept describes a geometric locus of points equidistant from a fixed center?

Which concept describes a geometric locus of points equidistant from a fixed center?

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

Answer: (A)

A circle is defined as all points that are at the same distance from a fixed center. That constant distance is the radius, so every point on the circle sits the same distance away from the center, forming the round shape. In coordinates, if the center is (h, k) and the radius is r, the locus is described by (x − h)² + (y − k)² = r², which captures the idea of equidistance to the center. The other shapes come from different criteria: an ellipse is the set of points where the sum of distances to two fixed points (foci) is constant; a parabola is the set of points equidistant from a fixed point (focus) and a fixed line (directrix); a polygon is a closed figure made of straight-line segments, not a single fixed-distance locus.

A circle is defined as all points that are at the same distance from a fixed center. That constant distance is the radius, so every point on the circle sits the same distance away from the center, forming the round shape. In coordinates, if the center is (h, k) and the radius is r, the locus is described by (x − h)² + (y − k)² = r², which captures the idea of equidistance to the center.

The other shapes come from different criteria: an ellipse is the set of points where the sum of distances to two fixed points (foci) is constant; a parabola is the set of points equidistant from a fixed point (focus) and a fixed line (directrix); a polygon is a closed figure made of straight-line segments, not a single fixed-distance locus.