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

  1. IfthensoIfwe can eliminate theterm by setting

  2. IfthenIfwe can eliminate theterm by writing

Example: IfthenSetthenand