Circle

A circle is the plane curve consisting of all points at a fixed distance from a fixed center. That distance is its radius.

Radius: A radius is a line segment from a circle’s center to a point on its circumference, or its length. Every point on a circle lies one radius from its center.
Circle equation: A circle equation describes points at a fixed distance from a center, commonly as (x − h)² + (y − k)² = r². Its standard form encodes the center and radius directly.
Area of a circle: The area of a circle is the plane region it encloses, equal to π times the square of its radius. It quantifies the region bounded by the curve.
Ellipse: An ellipse is a closed plane curve whose points have a constant sum of distances from two fixed foci. A circle is the special ellipse whose two foci coincide.
Diameter: A diameter is a chord passing through a circle’s center; its length is twice the radius. It gives the longest straight-line distance across the circle.
Cartesian coordinate system: A Cartesian coordinate system assigns points numerical coordinates along perpendicular axes. Coordinates make a circle’s center and radius precise algebraic quantities.
Trigonometry: Trigonometry studies relationships between angles and side lengths, especially in triangles and periodic functions. The unit circle gives a geometric definition of sine and cosine.
Parabola: A parabola is a plane curve whose points are equally distant from a fixed focus and a fixed directrix. Unlike a circle, it is an open curve rather than a closed one.
Circumference: Circumference is the distance around a circle. It measures the circle’s boundary and equals its diameter multiplied by π.
Distance formula: The distance formula calculates the straight-line distance between two points from their coordinates. Applying it to the center yields the circle equation.

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