Circles definitions Flashcards
Circles definitions
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Conic Section A shape formed by intersecting a cone with a plane, resulting in figures like circles, ellipses, parabolas, and hyperbolas. Circle A set of all points in a plane that are the same distance from a fixed center point. Center The fixed point from which every point on a circle is equidistant, typically denoted as (h, k). 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, clearly showing the center and radius. General Form A circle's equation written as x² + y² + Dx + Ey + F = 0, requiring conversion to standard form for graphing. Completing the Square A method for rewriting quadratic expressions to reveal perfect square trinomials, essential for converting circle equations. Vertical Line Test A graphical method to determine if a curve is a function; a circle fails this test. Graph A visual representation of a circle on the coordinate plane, showing its center and radius. Constant A fixed value in an equation, often representing terms not involving variables, such as F in the general form. Horizontal Position The h-value in (h, k), indicating how far the center of a circle is from the y-axis. Vertical Position The k-value in (h, k), indicating how far the center of a circle is from the x-axis. Equation A mathematical statement representing the relationship between the variables and constants for a circle. Function A relation where each input has one output; circles are not examples of this due to multiple outputs for some inputs.
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