Thread: Polar Equations

Given the polar equation r=4/(2+2sin(x)).Find the Directrix,eccentricity and sketch the conic.

Hello, Gracy!

You're expected to know the general form for polar conics.

. . . where = eccentricity

And these rules: .

Given the polar equation: .
Find the directrix, eccentricity and sketch the conic.

We have: .

Since , we have a parabola with its focus is at the pole (origin).

Plot a few points: .

The graph looks like this:

Code:

                     2|
          - - - - - - + - - - - - -
                      |
                     1|
                     ***
                *     |     *
             *        |        *
      ------*---------+---------*------
                      |
           *          |          *
                      |

The focus is 1 unit from the vertex.
. . Hence, the directrix is also 1 unit from the vertex.
It is the horizontal line:
. . Converting to polars: .