Given 4/ (-2 - cos(theta))

what is the distance between the pole and the directrix?

  the distance from pole to directrix is 4 units

Step-by-step explanation:

Rewritten to the form ...

  r = ed/(1+e·cos(theta))

you find ..

  ed = 4/-2 = -2 . . . . . where d is the distance from the pole to the directrix

  e = -1/-2 = 1/2 . . . . . the eccentricity

so d = ed/e = -2/(1/2) = -4 and the ellipse has the equation ...

  r = (1/2)(-4)/(1 + 1/2·cos(theta))

The directrix is a vertical line 4 units from the focus in the -x direction.

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared