# 第十八單元 平面上之參數方程式. Parametric Equations A plane curve is determined by a pair of parametric equations t, Called the parameter, as measuring time.

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Parametric Equations A plane curve is determined by a pair of parametric equations t, Called the parameter, as measuring time

Example Eliminate the parameter in Solution

Example Solution

Example

Differentiation for parametric curve Theorem

Example

Area

Example

Some Famous Curves www.chit.edu.tw/mathmet

Some Famous Curves

> with(plots): > g1:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=0..40],numpoints=400,frames=40, scaling=unconstrained): g2:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=-0.6..-0.1],color=black,numpoints=400,frames=40, > scaling=unconstrained): g3:=animatecurve([3*t/(1+t^3),3*t^2/(1+t^3),t=-100..-1.6],color=blue,numpoints=400,frames=40,scaling=unconstrained): display(g1,g2,g3);

Swallowtail Catastrophe Curve

graph

Ovals of Cassini

Witch of Agnesi www.chit.edu.tw/mathmet

Newton’s Parabola

Newton’s Parabola (animator)

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