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M408M Learning Module Pages
Main page Chapter 10: Parametric Equations and Polar CoordinatesLearning module LM 10.1: Parametrized Curves:3 kinds of functions, 3 kinds of curvesThe cycloid Visualizing parametrized curves Tracing curves and ellipses Lissajous figures Learning module LM 10.2: Calculus with Parametrized Curves:Learning module LM 10.3: Polar Coordinates:Learning module LM 10.4: Areas and Lengths of Polar Curves:Learning module LM 10.5: Conic Sections:Learning module LM 10.6: Conic Sections in Polar Coordinates:Chapter 12: Vectors and the Geometry of SpaceChapter 13: Vector FunctionsChapter 14: Partial DerivativesChapter 15: Multiple Integrals |
Tracing curves and ellipsesWe already saw that $x=\cos(t)$, $y=\sin(t)$ gives a circle traced counter-clockwise. In this demonstration, we'll look at something slightly more complicated:$$x(t) = a\cos(t) + h, \qquad y(t)=b\sin(t)+k,$$where $a$, $b$, $h$ and $k$ are numbers that you specify.
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