$\"\"$

The equation is $\"\"$ .

$\"\"$

Compare this polar equation with standard form $\"\"$ .

Where $\"\"$ and $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

$\"\"$ .

Since $\"\"$ , so the conic is ellipse.

Directrix is parallel to the polar axis at a distance $\"\"$ below the pole.

The directrix is $\"\"$ .

$\"\"$

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

\ \

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

\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \

The vertices are at $\"\"$ and $\"\"$ .

The center of the ellipse is is point of vertices is $\"\"$ .

Graph:

(1) Graph the polar co-ordinates.

(2) Plot the points.

(3) Connect the points to a smooth curve.

$\"\"$

The conic is ellipse.

The directrix is $\"\"$ .

Plot the vertices are $\"\"$ , $\"\"$ and center is $\"\"$ .

$\"\"$ .