Question

When the axes are rotated through an angle find the transformed equation
of 3+ 10xy + 3y = 9.​

Answer 1

Answer:

Step-by-step explanation:

When axes are rotated through 45  

0

 ,

x=xcosθ−ysinθ=  

2

​  

 

x−y

​  

 

y=xsinθ−ycosθ=  

2

​  

 

x+y

​  

 

3x  

2

+3y  

2

+2xy=2⇒3(  

2

​  

 

x−y

​  

)  

2

+3(  

2

​  

 

x+y

​  

)  

2

+2(  

2

x  

2

−y  

2

 

​  

)=2

3(x  

2

+y  

2

−2xy)+3(x  

2

+y  

2

+2xy)+2x  

2

−2y  

2

=4

4(2x  

2

+y  

2

)=4

⇒2x  

2

+y  

2

=1