$\"\"$

The polar equation is $\"\"$ .

Identify the type of conic, rewrite the equation in the form

$\"\"$ is a conic,

where $\"\"$ is the eccentricity and $\"\"$ is the distance between

the focus(pole) and the directrix.

Consider $\"\"$ .

Divide numerator and denominator by 2.

$\"\"$

$\"\"$ .

Compare it with $\"\"$ .

$\"\"$ .

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

$\"\"$

Graph the above polar equation using some polar coordinates.

For $\"image\"$ , $\"\"$ .

For $\"\"$ , $\"\"$ .

Make a table for a different values of $\"image\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"image\"$	$\"\"$	\ $\"image\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \

$\"\"$

Graph:

Draw the polar coordinate plane.

Plot the polar coordinates found in the table.

Connect the points with smooth curve.

$\"\"$

Observe the graph:

The polar equation represents an ellipse.

$\"\"$

The conic represents an ellipse.

Graph the equation $\"\"$ .

$\"\"$