Eliminate the Parameter definitions Flashcards
Eliminate the Parameter definitions
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Parametric Equations A pair or set of equations expressing variables as functions of a third variable, often t, to describe curves or motion. Parameter An independent variable, typically t, used in parametric equations to generate corresponding x and y values. Rectangular Equation An equation involving only x and y, obtained by eliminating the parameter from parametric equations. Elimination of the Parameter The process of rewriting parametric equations as a single equation in x and y by removing the parameter. Substitution Method A technique where one equation is solved for the parameter and substituted into the other to eliminate the parameter. Restriction on t A limitation on the values the parameter can take, often affecting the portion of the graph represented. Orientation The direction in which a curve is traced as the parameter increases. Pythagorean Identity A trigonometric relationship, such as sin²(t) + cos²(t) = 1, used to eliminate the parameter in trig-based parametric equations. Conic Section A curve formed by the intersection of a plane and a cone, such as a parabola or ellipse, often resulting from eliminating the parameter. Ellipse A conic section represented by an equation like x² + (y/3)² = 1, often arising from parametric equations with trigonometric functions. Parabola A conic section represented by an equation like y = x² - 3, commonly resulting from eliminating the parameter in certain parametric equations. Inverse Trigonometric Function A function such as arccos(x) or arcsin(x), which can appear when attempting to eliminate the parameter in trig-based parametric equations. Graphing The process of plotting points generated by parametric equations to visualize the curve or motion described. Square Root An operation often present in parametric equations, requiring t to be non-negative to avoid imaginary numbers. System of Equations A set of equations, such as x(t) and y(t), that can be manipulated together to eliminate the parameter.
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