   Chapter 12.6, Problem 41E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Families of Conics Graph the conics r = e / ( 1 − e cos θ ) with e = 0.4 , 0.6 , 0.8 , and 1.0 on a common screen. How does the value of e affect the shape of the curve ?

To determine

To sketch:

The conics r=e/(1ecosθ) with e=0.4,0.6,0.8, and 1.0 on a common screen and determine how value of e affects the shape of curve.

Explanation

Approach:

The steps written below describe how the graph of the Families of Conics is obtained.

Step 1: Turn on the graphing calculator.

Figure (1)

Step 2:Press MODE.

Using arrow buttons to navigate to POL and ENTER to select this option. This enables graphing in polar coordinates.

Figure (2)

If Radian is not selected then using arrow buttons navigate to Radian and ENTER to select radian mode.

Step 3: Press Y= and enter the equation of the conic for e=0.4.

Figure (3)

Figure (4)

Press GRAPH to plot the conic.

Figure (5)

The graph might appear too small or may not fit the whole screen depending on the setting for max and min values for x-axis and y-axis. To adjust these setting press WINDOW.

Figure (6)

Don’t adjust the settings to fit the graph to the calculator screen as we expect conic to grow wider with increasing e. We can adjust the settings after we have finished plotting the conics for all given values of e.

Step 4: Press Y= and enter the equation of conic for e=0.6 and press GRAPH.

Figure (7)

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