Question

what should be added to x²-3y²-2z²+5xy to obtain 3x²+3y²-2z²+10xy​

Answer 1

Correct option is

B

2X

2

+Y

2

=1

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

#xoLegendxBabuxo