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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.