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

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
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:
$Xmin=-7,Xmax=7,X\text{Scale}=1,Ymin=-7\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}Y\text{Scale}=1$
e) press the [GRAPH] key to plot the graph.
The graph: