MA 141 Study Guide - Final Guide: Ellipse, Parametric Equation, Cartesian Coordinate System

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We have discussed several di erent types of functions. It turns out that we can describe such curves using a pair of functions, one for each variable. Def: let f (t) and g(t) be two functions de ned on the interval t [a, b]. Then the curve in the xy-plane given by (x, y) = (f (t), g(t)) , t [a, b] is called a parametric curve, and t is the parameter along the curve. Given a parametric curve with x = f (t) and y = g(t), we can solve both equations for t and set them equal to each other or substitute one into the other. Ex: let x = t + 1 and y = t2. Find the cartesian equation (eliminate the parameter t). If x = t + 1, then t = x 1. This is a vertical parabola centered at (1, 0).

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