Exploring Analyic Geometry with Mathematica®

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Eliminate Linear Terms

elimlin.html

Exploration

Show that applying the change in variables

"elimlin_1.gif" and "elimlin_2.gif"

to the quadratic equation "elimlin_3.gif" yields the quadratic

"elimlin_4.gif"

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

"elimlin_5.gif"


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