MTH301 Practice Questions Lectures 23-45 by MS

Solutions of Practice Questions

Lecture No. 23 To 45

Q1. Find all possible polar co-ordinates representations of the point P whose

rectangular co-ordinates are (3 2, 3 2)

Solution

We have

x= 3 2 and y 

For polar coordinate P r 

(3 2) ( 3 2) r x y

tan tan ( 1) y x

The point P (3 2, 3 2) lies in the fourth quadrant

When

r

When r

Q1. 1 cos

r

graph of this curve about initial line.

Solution

Symmetry about initial line

As we know, cos( cos so equation of a curve remains same if  is replaced

by   . So the curve is symmetrical about initial line.

Q2. 2 cos2

r a

Solution

cos 2( cos 2 cos2 cos2 sin 2 sin 2 cos(2 )

So equation of a curve remains same if  is replaced by  . So the curve

is symmetrical about y-axis.

Q3. 8sin 2

r

Solution

sin 2( sin 2 sin 2 cos2 cos2 sin 2 sin(2 )

So equation of a curve does not remain same if  is replaced by  . So

the curve is not symmetrical about y-axis.

Lecture#25

Q1. Use double integrals in polar co-ordinates to find area of the region bounded by the

curve 7cos r

Solution

Here 7cos r is a circle of radius 7 2 and center at 7 ,0