I have only worked with ellipses aligned with the x or y axis. However, how can I approach the following:
Suppose we have an ellipse centered at the origin of the following form
$$ax^2 + b xy +c y^2 + d = 0$$
How would I go about finding the axes on which it lies. As clearly this will be a rotated ellipse.
Best Answer
Using Derivation of the rotation formula, find $\theta$ to remove $xy$ from the equation.
Here $x=x'\cos \theta-y'\sin \theta$ and $y=x'\sin\theta +y'\cos\theta$
So, $x'=x\cos \theta+y\sin \theta,y'=y\cos \theta-x\sin \theta$.