is to let
which corresponds to a rotation of the axes through an angle , in order to eliminate the term in . When you do this, it leads to the value of given by
You then complete the squares for and to get the equation in the required form.
In the example you've been given:
But this doesn't seem to give straightforward (i.e. easy) values for and ( , for instance).
Are you sure you have the right numbers here?