Please help with coordinate axes rotation!

Question

The exact question was:

"Rotate the coordinate axes to eliminate the xy term.

2x² + 2(sqrt3)xy + 4y² - 8 = 0"

 

(sqrt= square root)

 

 

Answer 1

For a conic in form Ax^2 + Bxy +Cy^2 +Dx+Ey+F=0

 

Rotation about an angle 0.5invcot(A-C)/B  eliminates the xy term.

 

So in this case the angle is 0.5cot-1/sqrt3 =-pi/6...30 degrees clockwise

 

This is a formula you can memorize for GRE Math Subject test.  Its derivation can be found at http://en.wikipedia.org/wiki/Rotation_of_axes