Question

Sketch the curve and find the area that it encloses.

r = 3 + 2 cos θ

Answer 1

Step 1 :

The curve equation is .

Construct a table for different values of .

0	5
	4.732
	4.414
	4
	3
	2
	1
	4.586
	3
	4
	4.732

 

Answer 2

Contd........

Step 2 :

Graph :

(1) Graph the polar co-ordinates.

(2) Plot the points.

(3) Connect the points with a smooth curve.

Graph of the curve is :

Step 3 :

Area of the region enclosed by the curve is .

The boundaries of the curve are .

Area of the region enclosed by the curve :

Area of the region enclosed by the curve is square units.

Solution :

Graph of the curve is :

Area of the region enclosed by the curve is square units.