Final answer:
To write a polar equation for a conic with the given characteristics, we first need to determine the type of conic. In this case, since the eccentricity (e) is equal to 1.6, which is greater than 1, the conic is a hyperbola.
Step-by-step explanation:
To write a polar equation for a conic with the given characteristics, we first need to determine the type of conic. In this case, since the eccentricity (e) is equal to 1.6, which is greater than 1, the conic is a hyperbola.
The general polar equation for a hyperbola is r = (ed)/(1+ecos(theta)), where r is the distance from the pole, e is the eccentricity, d is the distance from the pole to the directrix, and theta is the angle between the polar axis and the radius vector.
Given that the directrix is y = 4, we can substitute d = 4 into the equation:
r = (1.6 * 4)/(1 + 1.6cos(theta))