# Find angle to eliminate cross product term

1. Nov 22, 2009

### africanmasks

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. 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)?

2. Nov 22, 2009

### HallsofIvy

Staff Emeritus
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.

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