Step 1:

(a)

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

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

$\"\"$

Take out 6 common from the denominator.

$\"\"$

Now compare the above equation with standard form.

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

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

Step 2:

(b)

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

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

Step 3:

(c)

The value in the numerator is $\"\"$ .

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

$\"\"$

The ellipse equation is $\"\"$ .

The directrix is parallel to the polar axis $\"\"$ .

So the directrix of the ellipse is $\"\"$ .

Step 4:

(d)

The polar equation is $\"\"$ .

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 ellipse.

(d)