A curve called the folium of Descartes can be represented by the parametric equations x =3t/(1 + t 3 )and y =3t2/( 1 + t3). (a) Convert the parametric equations to polar form. (b) Sketch the graph of thepolar equation from part (a). (c) Use a graphing utility to approximate the area enclosed by the loop of the curve.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 31E
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A curve called the folium of Descartes can be represented by the parametric equations

x =3t/(1 + t 3 )and y =3t2/( 1 + t3).

(a) Convert the parametric equations to polar form. (b) Sketch the graph of thepolar equation from part (a). (c) Use a graphing utility to approximate the area enclosed by the loop of the curve.

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