   Chapter 10.3, Problem 61E

Chapter
Section
Textbook Problem

Folium of Descartes Consider the parametric equations x = 4 t 1 + t 3   and   y = 4 t 2 1 + t 3 . (a) Use a graphing utility to graph the curve represented by the parametric equations.(b) Use a graphing utility to find the points of horizontal tangency to the curve.(c) Use the integration capabilities of a graphing utility to approximate the arc length of the closed loop. (Hint: Use symmetry and integrate over the interval 0 ≤ t ≤ 1 .)

(a)

To determine

To-graph: The parametric equations, x=4t1+t3 and y=4t21+t3.

Explanation

Given:

The parametric equations, x=4t1+t3 and y=4t21+t3.

Graph:

Consider the parametric equations, x=4t

(b)

To determine

To-determine: The points of horizontal tangency to the curve in part (a) by the use of graphing utility.

(c)

To determine

To-calculate: The arc length of the curve in part (a) by the use of graphing utility.

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