Question

find the angle through which axis to be rotated to to remove xy terms from the equation aX square + 2h X y + ay square is equal to zero​

Answer 1

Answer:

Explanation:

et  axes  be  rotated  through  an  angle  ϕ, then old co-ordinates are

x=x  

1

cosϕ−y  

1

sinϕ

y=x  

1

sinϕ+y  

1

cosϕ

∴(x  

1

cosϕ−y  

1

sinϕ)  

2

+2  

3

​

(x  

1

cosϕ−y  

1

sinϕ)(x  

1

sinϕ+y  

1

cosϕ)−(x  

1

sinϕ+y  

1

cosϕ)  

2

=2a  

2

 

coefficient  of x  

1

y  

1

is

−2cosϕsinϕ+2  

3

​

(cos  

2

ϕ−sin  

2

ϕ)−2cosϕsinϕ=0

2  

3

​

(cos2ϕ)=2sin2ϕ

tan2ϕ=  

3

​

 

⇒2ϕ=  

3

π

​

 

ϕ=  

6

π

​

 

∴ angle  through  which  it  is  to  be  rotated  is  

6

π

​