Question

Find a polar equation of the conic with its focus at the pole.

Conic                                   Eccentricity                             Directrix

Ellipse                                   e = 1/2                                     y = 1

Answer 1

Step 1:

The eccentricity is and directrix is .

The directrix is horizontal and above the pole, then the polar equation of the conic is .

The distance between pole and directrix is

Now substitute and in the polar equation .

Solution :

The polar equation of the conic is .