Question

Use a graphing utility to graph the polar equation. Identify the graph and find its eccentricity.

Answer 1

Step 1:

The polar equation .

Graph the above polar equation using some polar coordinates.

Construct a table for different values of .

Graph:

Draw the polar coordinate plane.

Plot the  polar coordinates found in the table.

Connect the points with smooth curve.

Step 2:

The polar equation .

To identify the type of conic, rewrite the equation in the form .

where is the eccentricity and is the distance between the focus(pole) and the directrix.

Compare with

Since , the equation represents a parabola.

Solution:

represents a parabola.

Eccentricity .