Question

The transformed equation of the curve x2+2√3xy-y2-8 when the axes are rotated through an angle π/6 is

Answer 1

Answer:

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

Answer 2

Step-by-step explanation:

1 is the correct ans of the given ques