Find angle to eliminate cross product term

[africanmasks]

Homework Statement

If you make the change of variables:

x= ucos(\theta)-vsin(\theta)
y= usin(\theta)+vcos(\theta)

where the angle 0 \leq \theta <\pi/2 is chosen in order to eliminate the cross product term in:

4x²+8xy+6y²=30

What is the angle you would use?

Homework Equations

The Attempt at a Solution

I have no idea. Would you find when the 8xy term (in terms of the new variables) is zero (solve for theta)?

 

[HallsofIvy]

Not just the xy term. Each of the three terms will have "uv" in them.

Replace x with u cos(\theta)- v sin(\theta) and y with u sin(\theta)+ v cos(\theta) in 4x^2+ 8xy+ 6 y^2. There will be "uv" terms in all three of those terms. Add then up and choose \theta to make the coefficient of uv equal to 0.