Question

Use a graphing utility to graph the polar equation when (a) e = 1,  (b) e = 0.5, and (c) e = 1.5. Identify the conic.

Answer 1

Step 1:

The polar equation is .

(a) Find the equation of conic by substituting in .

Since , is parabola.

Step 2:

(b) Find the equation of conic by substituting in .

Since , is ellipse.

Step 3:

(c) Find the equation of conic by substituting in .

Since , is hyperbola.

Step 4:

Graph the polar equations.

Observe the graph: when the conic is parabola.

when the conic is ellipse.

when the conic is hyperbola.

Solution:

Graph of three polar equations:

.