Question

Write the appropriate rotation formulas so that in a rotated system the equation has no x’y’-term
10x^2-4xy+6y^2-8x+8y=0

Answer 1

You want to remove the 'xy' term in the new formulation, which is different from --- eg finding the principal axis.

Algebra heavy, and therefore way above my pay-grade....so i looked it up



Using the rotation matrix

\(R(\theta) = \begin{bmatrix}
\cos \theta & \sin \theta \\
- \sin \theta & \cos \theta
\end{bmatrix}\)

And:

\(\mathbf x = R(\theta) \mathbf {x'}= \begin{bmatrix}
\cos \theta & \sin \theta \\
- \sin \theta & \cos \theta
\end{bmatrix} \mathbf {x'}\)



Hope you get the same result: \(\theta = -\frac{\pi}{8}\)

stuff that into the original matrix and you might get the right answer :)

maybe 🤔

Answer 2

da link