   Chapter 10.6, Problem 4E

Chapter
Section
Textbook Problem

# Graphical Reasoning In Exercises 1–4, use a graphing utility to graph the polar equation when (a) e = 1, (b) e = 0.5, and (c) e = 1.5. Identify the conic. r = 2 e 1 + e   sin   θ

(a)

To determine

To graph: The polar equation, r=2e1+esinθ when e=1 and to identify the conic.

Explanation

Given:

The polar equation is r=2e1+esinθ, where e=1.

Graph:

Consider the polar equation,

r=2e1+esinθ.

Substitute e=1 in the above equation,

r=21+sinθ

Use following steps in TI-83 graphing calculator to obtain graph of the above equation.

Step 1: Press the MODE button.

Step 2: Press the down arrow key twice to “Radian” and press ENTER key.

Step 3: Press down the arrow key to “Func”. Then press right key to “Pol” and press ENTER again.

Step 4: Press CLEAR key.

Step 5: Press “Y=” key.

Step 6: Enter the equation, 2÷(1+sinθ).

Step 7: Press the WINDOW key and set the values as follows:

θmin=0θmax=6

(b)

To determine

To graph: The polar equation, r=2e1+esinθ when e=0.5 and to identify the conic.

(c)

To determine

To graph: The polar equation, r=2e1+esinθ when e=1.5 and identify the conic.

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