Step 1:

The polar equation is $\"\"$ .

Convert the given polar equation into standard form of the polar equation $\"\"$ .

$\"\"$

Take out 3 as common from the denominator.

$\"\"$

Now compare the above equation with standard form. $\"\"$ and $\"\"$ .

The eccentricity of the conic equation is $\"\"$ .

As eccentricity $\"\"$ , the given conic section is a hyperbola.

$\"\"$

Directrix is perpendicular to the polar axis at a distance $\"image\"$ units to the left of the pole.

Then the directrix is perpendicular to the polar axis at a distance $\"\"$ units to the left of the pole.

The directrix is $\"\"$ .

Find the vertices, take $\"\"$ and $\"\"$ .

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

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

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

Graph:

(1) Graph the polar co-ordinates.

(2) Plot the points.

(3) Connect the points to a smooth curve.

Solution :

(a) The eccentricity of the conic equation is $\"\"$ .

(b) The given conic section is a hyperbola.

(d) The vertices are $\"\"$ and $\"\"$ .