$\"\"$

The equation is $\"\"$ .

$\"\"$

Compare the polar equation with $\"\"$ .

Here $\"\"$ and $\"\"$ .

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

$\"\"$

Since $\"\"$ , the conic is hyperbola.

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

$\"\"$

The directrix is $\"\"$ .

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

\ \

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

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

The vertices of the equation are at $\"\"$ and $\"\"$ .

Therefore,the vertices are $\"\"$ and $\"\"$ .

The center of the equation is the mid point of the vertices.

Center is $\"\"$ .

Graph:

(1) Graph the polar co-ordinates.

(2) Plot the points.

(3) Connect the points to a smooth curve.

$\"\"$

The conic is hyperbola.

The directrix is $\"\"$ .

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

$\"\"$ .