**Problem : **
Is the directrix of the conic horizontal or vertical? Does it lie to
the left, the right, above, or below the pole? Conic: *r* =

The directrix is horizontal, and below the pole.

**Problem : **
What type of conic is the following: *r* = ?

*r* = = .

*e* = > 1, so the conic is a hyperbola.

**Problem : **
What type of conic is the following: *r* = ?

*r* = = .

*e* = < 1, so the conic is an ellipse.

**Problem : **
Find the vertex (or vertices) of the conic *r* = .

*e* = 1, so the conic is a parabola, and it has a horizontal directrix above
the pole. Because its directrix is horizontal, its axis must be vertical.
So the vertex will occur on the line

*θ* = .

(*r*,) = (2,) is the vertex of the parabola. Note:
Another way to find the vertex is to use the fact that

*p*, the distance from
the focus to the directrix, is known to be

4 in this problem.

**Problem : **
Find *a*, *b*, and *c* of the conic *r* = .

*e* = 2, so the conic is a hyperbola. The directrix is vertical and to the left
of the pole. The transverse axis is horizontal. The vertices are at

(- 6, 0) and

(2, *Π*). So the transverse axis is

8 units long, so

*a* = 4.
Therefore

*c* = 8, and

*b* = 4.

**Problem : **
Express the parabola whose focus is the pole and whose horizontal directrix is 5
units above the pole in polar form.

*r* = .