Question

"Consider the ellipse (x² / 4) + (y² / 1) = 1. What is the equation describing this ellipse after it has been rotated thirty degrees counterclockwise?" how do I figure this out??

Answer 1

use counterclockwise rotation matrix for xy-plane

\[R=\left[\begin{matrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{matrix}\right]\]

Answer 2

Ok thanks