Exploring Analyic Geometry with Mathematica®

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Circle Through Three Points

cir3pts.html

Exploration

Show that the equation of the circle through the three points (0,0), (a,0) and (0,b) is "cir3pts_1.gif".

Approach

Find the quadratic (circle) through the three points, then convert it to an 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

Construct the quadratic.

Clear[a,b];
Q=Quadratic2D[Point2D[0,0],Point2D[a,0],Point2D[0,b]]

"cir3pts_2.gif"

Simplify and convert the quadratic to an equation.

Clear[x,y];
Equation2D[
   Quadratic2D @@ SimplifyCoefficients2D[List@@Q],
   {x,y}]

"cir3pts_3.gif"


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