$\"\"$

The equation is $\"\"$ .

From the trigonometric identity : $\"\"$ .

$\"\"$

The polar coordinates are related to Cartesian coordinates by the equation $\"\"$ .

Where $\"\"$ .

$\"\"$ .

Therefore, $\"\"$ is a hyperbola ,center $\"\"$ ,foci on $\"\"$ axis.

$\"\"$

The equation $\"\"$ represents a hyperbola with center $\"\"$ , foci on $\"\"$ axis.