   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 4 t ,   y = t + 4

To determine

To graph: The parametric equation, x=e4t,y=4+t and mark the orientation of the curve also convert the equation in rectangular form.

Explanation

Given:

The parametric equation is x=e4t,y=4+t.

Graph:

Consider the parametric equation, x=e4t,y=4+t.

Plot the graph of the values of x and y by letting values for t and constructing a table.

First, consider the equation x=e4t.

For t=0, substitute 0 for t in x=e4t.

x=e4×0x=e0x=1

For t=0.5, substitute 0.5 for t in x=e4t.

x=e4×0.5x=e2x=7.3890

For t=1, substitute 1 for t in x=e4t.

x=e4×(1)x=e4x=0.0183

For t=2, substitute 2 for t in x=e4t.

x=e4×(2)x=e8x=0.000335

Secondly, now consider the equation y=4+t.

For t=0, substitute 0 for t in y=4+t.

y=4+0y=4

For t=0.5, substitute 0.5 for t in y=4+t.

y=4+0

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