   Chapter 12.6, Problem 42E ### 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 ( a ) Graph the conics r = e d ( 1 + e sin θ ) for e = 1 and various values of d . How does the value of d affect the shape of the conic ? ( b ) Graph these conics for d = 1 and various values of e . How does the value of e affect the shape of the conic?

To determine

a)

To sketch:

The conics r=ed(1+esinθ) for e=1 and various values of d. Also, find how the value of d affects the shape of the conic.

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 d=1

Figure (3)

Figure (4)

While entering the equation for d=1 to enter 1 in the numerator press () button to enter the negation sign.

Press GRAPH to plot the conic.

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 (5)

Figure (6)

Step 4: Press Y= and enter the equation of conic for d=0

To determine

b)

To sketch:

The conics r=ed(1+esinθ) for d=1 and various values of e. Also, find how the value of e affects the shape of the conic.

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