   Chapter 10, Problem 30RE

Chapter
Section
Textbook Problem

Using Parametric Equations In Exercises 27-34, sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. x = e t − 1 ,   y = e 3 t

To determine

To calculate: The corresponding rectangular equation by eliminating the parameters and plot the graph of the rectangular equation when the parametric equations are x=et1, y=e3t.

Explanation

Given:

The parametric equations are x=et1, y=e3t

Calculation:

Consider the parametric equations.

x=et1

y=e3t

To graph the parametric firstly find some values of x and y for different values of t.

For t=

x=e1=1y=e=0

For t=0

x=e01=0y=e3×0=1

For t=0.13

x=e0.131=0.13y=e3×0.13=1.5

For t=0.23

x=e0.231=0.25y=e3×0

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