Given: r = 4/-2-costheta
What type of directrix does this conic have?
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Vertical
Horizontal
Oblique
This conic does not have a directrix.
To determine the type of directrix, we need to identify the conic section that is described by the given equation.
Let's analyze the given equation: r = 4/-2cos(theta).
In this equation, we have two variables: r and theta. Here, r represents the distance from the origin to a point on the curve, and theta represents the angle between the positive x-axis and the line connecting the origin to the point on the curve.
By rearranging the equation, we have: r * cos(theta) = -2.
Now, let's simplify this equation by substituting r^2 * cos^2(theta) = x^2 and r^2 * sin^2(theta) = y^2 (where x and y are the Cartesian coordinates).
We get: x^2 = -2 cos(theta) and y^2 = -2 sin(theta).
Since both x^2 and y^2 are negative, we can deduce that this equation represents an ellipse.
Now, in ellipse, there is no directrix. The directrix is a characteristic of other conic sections such as parabolas or hyperbolas.
Therefore, the correct answer is: This conic does not have a directrix.