Answer:
Hyperbola
Step-by-step explanation:
The polar equation of a conic section with directrix ± d has the standard form:
r=ed/(1 ± ecosθ)
where e = the eccentricity.
The eccentricity determines the type of conic section:
e = 0 ⇒ circle
0 < e < 1 ⇒ ellipse
e = 1 ⇒ parabola
e > 1 ⇒ hyperbola
Step 1. Convert the equation to standard form
r = 4/(2 – 4 cosθ)
Divide numerator and denominator by 2
r = 2/(1 - 2cosθ)
Step 2. Identify the conic
e = 2, so the conic is a hyperbola.
The polar plot of the function (below) confirms that the conic is a hyperbola.
