The general equation of a conic section is
It is often useful to eliminate the
term. This can be done by rotating the
coordinate axes onto a new set of axes
To see this substitute
into (1). The coefficient of
is
which simplifies to
To eliminate the XY term we must have this coefficient equal to zero, so that
-
If
then
so
Ifwe can eliminate theterm by setting
-
If
then
Ifwe can eliminate theterm by writing
Example: If
then
Set
then
and
becomes
or
