Final answer:
To sketch the conic given the equation in polar coordinates r = 2/(1 - cos(θ)), we can convert it to Cartesian coordinates and plot the shape on the Cartesian plane. The vertices of the conic can be found by identifying the points where the x-coordinate is at its maximum and minimum value.
Step-by-step explanation:
To sketch the conic with the equation r = 2/(1 - cos(θ)), we can rewrite it in Cartesian coordinates. Using the trigonometric identities x = r * cos(θ) and y = r * sin(θ), we can substitute these equations into the given equation to obtain x = 2 * cos(θ)/(1 - cos(θ)) and y = 2 * sin(θ)/(1 - cos(θ)).
Now, we can plot the polar coordinates (r, θ) on the Cartesian plane. Choose various values of θ and calculate the corresponding x and y coordinates. Plot these points and join them to form the shape of the conic.
The vertices of the conic can be found by determining the points where the x-coordinate is at its maximum and minimum value. These points correspond to the vertices of the conic.