Circles definitions Flashcards
Circles definitions
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Conic Section A shape formed by slicing a three-dimensional cone with a two-dimensional plane, resulting in figures like circles. Circle A set of all points in a plane that are equidistant from a fixed point known as the center. Center A fixed point from which every point on a circle is the same distance away. Radius The constant distance from the center of a circle to any point on its circumference. Origin The point (0,0) on a coordinate plane, often used as the center for circles in standard equations. Standard Form An equation format for circles: (x-h)² + (y-k)² = r², revealing the center and radius directly. General Form A circle's equation written as x² + y² + Dx + Ey + F = 0, requiring manipulation to find center and radius. Completing the Square A method used to rewrite quadratic expressions, essential for converting a circle's general form to standard form. Vertical Line Test A graphical method to determine if a curve represents a function; circles fail this test. Graph A visual representation of a circle on the coordinate plane, showing its center and radius. Equation A mathematical statement expressing the relationship between the coordinates of points on a circle. Constant A fixed value in a circle's equation, often representing terms not involving variables. Coordinate Plane A two-dimensional surface defined by x and y axes, used for plotting circles and their properties. Horizontal Position The x-coordinate of a circle's center, denoted as h in the standard form equation. Vertical Position The y-coordinate of a circle's center, denoted as k in the standard form equation.
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