Question

R={8}/{3+3 cos θ} Sketch the conic and label the vertices.

Answer 1

The equation r = 8/(3 + 3 cos θ) represents a circle. To sketch the circle, plot points by substituting different values of θ into the equation and solving for r. The circle has a center at (0, 0) and a radius of 8/3 units.

Step-by-step explanation:

The equation r = \frac{8}{3 + 3 \cos \theta} represents a conic section called a circle.

To sketch the circle, you can plot points by substituting different values of \theta into the equation and solving for r. Here are the steps:

1. Choose values for \theta (e.g., 0°, 30°, 60°, 90°, etc.)
2. Calculate the corresponding values of r using the equation
3. Plot the points (r, \theta) on a graph
4. Connect the plotted points to form a smooth curve

The circle does not have vertices, but it has a center at (0, 0) and a radius of 8/3 units.