The polar equation is .

                  (Substitute e = 1)

Compare the equation with .

p = distance between the pole and the directix = 2.

So, the graph of the conic is at horizontal directix above the pole.

The polar function is .

Make the table of values to find ordered pairs that satisfy the function.

Choose random values for and find the corresponding values for r.

1.Draw a polar co-ordinate plane.

2.Plot the points.

3.Draw a smooth curve through those points. 

The above curve represents a parabola.

              (Substitute e = 0.5)

                  (Simplify)

Compare the equation with .

p = distance between the pole and the directix = 2.

So, the graph of the conic is at horizontal directix above the pole.

The polar function is .

Make the table of values to find ordered pairs that satisfy the function.

Choose random values for and find the corresponding values for r.

1.Draw a polar co-ordinate plane.

2.Plot the points.

3.Draw a smooth curve through those points. 

The above represents an ellipse.

              (Substitute e = 1.5)

                  (Simplify)

Compare the equation with .

p = distance between the pole and the directix = 2.

So, the graph of the conic is at horizontal directix above the pole.

The polar function is .

Make the table of values to find ordered pairs that satisfy the function.

Choose random values for and find the corresponding values for r.

1.Draw a polar co-ordinate plane.

2.Plot the points.

3.Draw a smooth curve through those points. 

The above curve represents a hyperbola.

Graph of the above equations are shown below :

If e = 1 the conic is parabola, if e = 0.5 the conic is ellipse and

if e = 1.5 the conic is hyperbola.

Graphs of the functions are shown below :