Answer:
(d) r = 3/(2 -3cos(θ))
Step-by-step explanation:
You want the equation that represents the hyperbola shown in the graph.
X-axis
The vertices are on the x-axis at points that are both to the left of the origin. That is, for θ = 0, the value of r will be negative, and for θ = π, the value of r will be positive.
The sign of r is determined by the sign of (2 ±3cos(θ)). It will only meet the required conditions for the coefficient of cos(θ) being negative.
The equation of the graph is r = 3/(2 -3cos(θ)), choice D.
