Question

Find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.)

Conic                                                  Eccentricity                                                  Directrix

Ellipse                                                   e = 1/2                                                           y = 1

Answer 1

Step 1:

Eccentricity and directrix .

The graph of polar equation of the form or is a conic,

where  is the eccentricity and  is the distance between the focus(pole) and the directrix.

Since the graph has a horizontal directrix, the equation is .

is the distance between pole and directrix.

Horizontal directrix above the pole is .

Substitute the values and in .

Solution:

Polar equation is .