Final Answer:
The directrix of the parabola given by the equation is A) r cos θ = 2.
Explanation:
The equation provided is in polar coordinates, represented as r = 2/cos θ, which can be rewritten as r cos θ = 2. In a polar coordinate system, the equation of a parabola in terms of r and θ has a directrix that is perpendicular to the axis of symmetry, which is given by the equation r = constant. Here, the equation r cos θ = 2 implies that the directrix of the parabola is r cos θ = 2, a line perpendicular to the axis of symmetry.
In polar coordinates, for a parabola represented by r = 2/cos θ, the focus of the parabola is at the pole (0,0), and the directrix is a line perpendicular to the axis of symmetry at a distance of 2 units from the pole along the line r cos θ = 2. This directrix acts as a point of reference regarding the parabola's reflective properties, where all points on the parabola are equidistant from the focus (pole) and the directrix (line r cos θ = 2) (option A).
Therefore, among the given options, the equation r cos θ = 2 correctly represents the directrix of the parabola given by the polar equation r = 2/cos θ, indicating the line that is perpendicular to the axis of symmetry and serves as a pivotal reference for the parabola's reflective properties in the polar coordinate system.