To calculate: The sections represented by the polar equation $r=\frac{18}{6-6\mathrm{cos}\theta}$ and graph it by the use of graphing utility.

Daniaal Sanchez
2021-03-07
Answered

To calculate: The sections represented by the polar equation $r=\frac{18}{6-6\mathrm{cos}\theta}$ and graph it by the use of graphing utility.

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Elberte

Answered 2021-03-08
Author has **95** answers

Step 1

The equation$r=\frac{18}{6-6\mathrm{cos}\theta}$ is not in standard form as the constant tern in the denominator is not 1.

To obtain 1 as the constant term in the denominator divide the numerator and denominator by 4.

Thus,

$r=\frac{18}{6-6\mathrm{cos}\theta}=\frac{3}{1-\mathrm{cos}\theta}$

The equation$r=\frac{3}{1-\mathrm{cos}\theta}$

is in the standard form of$r=\frac{ep}{1-e\mathrm{cos}\theta}.$

On comparing the provided equation to the standard form it can be obtained that$e=1.$

Since$e=1,$ thus the given polar equation represents a parabola.

Step 2

Now, use Ti-83 to plot the graph of the function:

a) Press the [MODE] key then select the polar function and the radian mode.

b) Press the [Y=] key, then there will appear the equations for y.

c) Enter the equations in$r}_{1$ .

Here,${r}_{1}=\frac{18}{6-6\mathrm{cos}\theta}.$

d) Press [WINDOW] and then edit the values as:

$Xmin=-7,Xmax=7,X\text{Scale}=1,Ymin=-7{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}Y\text{Scale}=1$

e) press the [GRAPH] key to plot the graph.

The graph:

The equation

To obtain 1 as the constant term in the denominator divide the numerator and denominator by 4.

Thus,

The equation

is in the standard form of

On comparing the provided equation to the standard form it can be obtained that

Since

Step 2

Now, use Ti-83 to plot the graph of the function:

a) Press the [MODE] key then select the polar function and the radian mode.

b) Press the [Y=] key, then there will appear the equations for y.

c) Enter the equations in

Here,

d) Press [WINDOW] and then edit the values as:

e) press the [GRAPH] key to plot the graph.

The graph:

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