Eliminate Linear Terms

elimlin.html

Exploration

Show that applying the change in variables

and

to the quadratic equation yields the quadratic

whose linear terms have vanished.

Approach

Apply the transformation rules directly to the quadratic equation.

Initialize

To initialize Descarta2D, select the input cell bracket and press SHIFT-Enter.

This initialization assumes that the Descarta2D software has been copied into one of the standard directories for AddOns which are on the Mathematica search path, $Path.

<<Descarta2D`

Solution

Apply the transformation rules to the equation.

Clear[a,c,d,e,f,x,y];
a*x^2+c*y^2+d*x+e*y+f /.
   {x->x-d/(2a), y->y-e/(2c)} //Expand