Parametric Sketches

Tuesday, 24 April 2018

3:03 PM

A curve in cartesian form  can be written parametrically as

 

 

Machine generated alternative text: The table below lists some commonly used parametrisations of conic sections. Conic section Cartesian equation Parametric equation btant Parabola Circle Ellipse Hyperbola 2 4ay = x 2 2 1 2 a 2 a b2 x(t) 2at at2 — a cos t y(t) — — asin t a cos t y(t) b sin t a sec t

Machine generated alternative text: Sketching parametrically defined curves We shall use some of the same ideas as we did in sketching curves given explicitly. o o o o o The domain refers to t and now range of x(t) gives x extent of the graph; range of gives y extent of graph; The x-intercepts are given by = 0, and the y-intercepts by = 0; Look for asymptotes; Locate any "nasty" points in the graph, mainly where x' (t) 0; Find where the graph has positive or negative slope.

 

 

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