Answer:
Choice B is correct
Step-by-step explanation:
The eccentricity of the conic section is given as 4 and thus the conic section is a hyperbola. Hyperbolas are the only conic sections with an eccentricity greater than 1.
Next, the directrix of this hyperbola is located at y = -6 implying that the hyperbola will be opening upwards. Consequently, the polar equation of this hyperbola will be of the form;
[tex]r=\frac{k}{1-4sin(theta)}[/tex]
The value of k in the numerator is the product of eccentricity and the absolute value of the directrix;
k= 4*6 = 24
The polar equation is thus given by alternative B
