Eliminating the xy Term in Conic Sections
The general equation of a conic section isIt is often useful to eliminate theterm. This can be done by rotating thecoordinate axes onto a new set of axes
To see this substituteinto (1). The coefficient ofiswhich simplifies toTo eliminate the XY term we must have this coefficient equal to zero, so that

IfthensoIfwe can eliminate theterm by setting

IfthenIfwe can eliminate theterm by writing
Example: IfthenSetthenand
becomesor