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.