The equation is .

Rewrite the above equation .

Compare the above equation with polar equation of conic .

Here and .

Since , the equation is hyperbola.

The directrix of the hyperbola is .

The general equation of hyperbola in rectangular form : .

The vertices lie on the transverse axis.

The vertices occur when and .

**Case 1 : **When .

Substitute in the above equation.

**Case 2 : **When .

Substitute in the above equation.

The polar coordinates of the vertices are and correspond to the rectangular coordinates are and .

The hyperbola’s center is the midpoint of the vertices .

The distance between the center and each vertex is .

The distance from the center to the focus at is .

Substitute corresponding values in the general equation of hyperbola.

Substitute corresponding values in .

The equation of hyperbola is .

The equation of hyperbola is .

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