$\"\"$

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

The standard form of the polar equation $\"\"$ .

(a)

$\"\"$

Compare the above equation with standard form.

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

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

As eccentricity $\"\"$ , the conic equation is hyperbola.

$\"\"$

The ellipse equation is $\"\"$ .

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

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

$\"\"$

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

$\"\"$

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.

$\"\"$ .

$\"\"$

(b)

When $\"\"$ is rotated by an angle $\"\"$ in counterclockwise direction, the resulting equation is $\"\"$ .

The equation is $\"\"$ .

Substitute $\"\"$ .

$\"\"$ .

Graph:

Graph of the equation $\"\"$ .

$\"\"$

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

The given conic section is a hyperbola.

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

$\"\"$

(b) Graph of the equation $\"\"$ is

$\"\"$