   Chapter 10.3, Problem 95E

Chapter
Section
Textbook Problem

# Using Parametric Equations(a) Use a graphing utility to graph the curve given by x = 1 − t 2 1 + t 2     and   y = 2 t 1 + t 2 ,   − 20 ≤ t ≤ 20 .(b) Describe the graph and confirm your result analytically.(c) Discuss the speed at which the curve is traced as t increases from -20 to 20.

(a)

To determine

To-graph: The parametric equations given as x=1t21+t2 and y=2t1+t2 where, 20t20.

Explanation

Given:

The parametric equations are given by, x=1t21+t2 and y=2t1+t2 over the interval 20t20.

Graph:

Consider the parametric equations, x=1t21+t2 and y=2t1+t2 over the interval 20t20

(b)

To determine
The description of the graph shown in part (a) and find the analytical result to confirm the graph (a).

(c)

To determine

To calculate: The speed at which the curve is traced as t increases from -20 to 20.

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