Question

write the polar equation of the conic for e = 1 , e = 0.5, and e = 1.5. Identify the conic for the given equation.Verify your answers with a graphing utility.

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:

.