Step 1: \ \

The polar equation is $\"\"$ . \ \

$\"\"$ \ \

Convert the equation into the conic form $\"\"$ . \ \

where $\"image\"$ is the eccentricity and $\"image\"$ is the distance between the focus(pole) and the directrix. \ \

$\"\"$ \ \

Compare with $\"\"$ . \ \

$\"\"$ \ \

Since $\"\"$ , the equation represents an ellipse. \ \

Step 2: \ \

Graph the above polar equation using some polar coordinates. \ \

Construct a table for different values of $\"\"$ .

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Graph:

Draw the polar coordinate plane.

Plot the polar coordinates found in the table.

Connect the points with smooth curve. \ \

$\"\"$ \ \

Observe the graph: The ellipse eccentricity $\"\"$ and distance $\"\"$ .

Solution: \ \

Eccentricity $\"\"$ . \ \

Distance $\"\"$ . \ \ \ \