$\"\"$

The equation is $\"\"$ .

$\"\"$

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

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

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

$\"\"$

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

Directrix is perpendicular to the polar axis at a distance $\"\"$ right to the pole.

The directrix is $\"\"$ .

$\"\"$

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

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

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

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

The center of the hyperbola is mid point of the vertices 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 $\"\"$ .

The center is at $\"\"$ .

$\"\"$ .