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Parametric Equations definitions

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  • Parametric Equations
    Expressions where two variables are written in terms of a third variable, often called the parameter.
  • Parameter
    A variable, typically t, used to define both x and y in a set of equations, guiding the generation of coordinate pairs.
  • Plane Curve
    A set of points in the xy-plane traced by parametric equations, which may form lines, parabolas, or more complex shapes.
  • Orientation
    The direction along a curve indicated by increasing parameter values, often shown with arrows on the graph.
  • Rectangular Equation
    An equation involving only x and y, obtained by eliminating the parameter from parametric equations.
  • Elimination of Parameter
    The process of removing the parameter from parametric equations to yield a direct relationship between x and y.
  • Parameterization
    The process of expressing a rectangular equation as two equations in terms of a parameter.
  • Domain Restriction
    A limitation on parameter values to avoid undefined or non-real results, such as negative values under a square root.
  • Pythagorean Identity
    A trigonometric relationship, such as sin²t + cos²t = 1, used to connect parametric equations involving trig functions.
  • Table of Values
    An organized list of parameter values and their corresponding x and y outputs, used for plotting parametric graphs.
  • Conic Section
    A curve, such as an ellipse or parabola, often represented by parametric equations and their rectangular forms.
  • Graph Orientation
    The sequence in which points are plotted as the parameter increases, determining the path's direction.
  • Substitution Method
    A technique where one equation is solved for the parameter and substituted into the other to eliminate the parameter.
  • Trigonometric Parameterization
    A method of expressing x and y using sine and cosine functions of a parameter, often for circles and ellipses.
  • Inverse Function
    A function, such as inverse cosine, used when solving for the parameter in terms of x or y during elimination.