Step 1:

The polar equation is $\"\"$ .

(a) Find the equation of conic by substituting $\"\"$ in $\"\"$ .

$\"\"$

Since $\"\"$ , $\"\"$ is parabola.

Step 2:

(b) Find the equation of conic by substituting $\"\"$ in $\"\"$ .

$\"\"$

Since $\"image\"$ , $\"\"$ is ellipse.

Step 3:

(c) Find the equation of conic by substituting $\"\"$ in $\"\"$ .

$\"\"$

Since $\"image\"$ , $\"\"$ is hyperbola.

Step 4:

Graph the polar equations.

$\"\"$

Observe the graph: when $\"\"$ the conic is parabola.

when $\"\"$ the conic is ellipse.

when $\"\"$ the conic is hyperbola.

Solution: \ \

Graph of three polar equations:

$\"\"$ .