The graph of r = -9 cos theta has which of the following characteristics?

"circle; diameter of 9; center at (-4.5,0)"

Step-by-step explanation:

The polar equation of a circle centered on an axis, would take the forms:

1. Positive x-axis

r = (diameter) Cos θ

2. Positive y-axis

r = (diameter) Sin θ

3. Negative x-axis

r = - (diameter) Cos θ

4. Negative y-axis

r = - (diameter) Sin θ

As we see from the equation given, the diameter is 9 and it is centered n negative x-axis. And the center is Diameter divided by 2. So negative x axis has the center at (-9/2, 0) = (-4.5, 0)

The first choice is correct.