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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.