Answer:
Choice D is correct
Step-by-step explanation:
The first step is to write the polar equation of the conic section in standard form by dividing both the numerator and the denominator by 2;
[tex]r=\frac{3}{1-cos(theta)}[/tex]
The eccentricity of this conic section is thus 1, the coefficient of cos θ. Thus, this conic section is a parabola since its eccentricity is 1.
The value of the directrix is determined as;
d = k/e = 3/1 = 3
The denominator of the polar equation of this conic section contains (-cos θ) which implies that this parabola opens towards the right and thus the equation of its directrix is;
x = -3
Thus, the polar equation represents a parabola that opens towards the right with a directrix located at x = -3. Choice D fits this criteria
