Question

Describe the graph of the polar equation and find the corresponding rectangular equation. Sketch its graph.

r = 3 sec θ

Answer 1

Step 1 :

The polar equation is .

Construct a table for different values of .

Step 2 :

Graph :

(1) Draw the polar co-ordinate plane.

(2) Plot the polar points.

(3) Connect the points to a straight line.

Step 3 :

The graph of the polar equation is not evident by simple inspection.

So convert it into rectangular form.

Conversion from polar to rectangular equation : and .

Consider .

The rectangular form of is .

Solution :

The graph of the polar equation is

The rectangular form of is .