/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 14.12.1 ] */

/* [wxMaxima: title   start ]
The conic section passing through five given points
   [wxMaxima: title   end   ] */

/* [wxMaxima: comment start ]
Creating five random integer points:
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
x1:random(100)-50;
y1:random(100)-50;
x2:random(100)-50;
y2:random(100)-50;
x3:random(100)-50;
y3:random(100)-50;
x4:random(100)-50;
y4:random(100)-50;
x5:random(100)-50;
y5:random(100)-50;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
pts:[[x1,y1],[x2,y2],[x3,y3],[x4,y4],[x5,y5]];
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
Here is the equation for the conic section. 
Why can we set the constant coefficient equal to 1?  - Can we?
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
eq: a*x^2+b*x*y+c*y^2+d*x+e*y+1;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
Creating the system of 5 equations:
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
sys:[at(eq=0,[x=x1,y=y1]),
    at(eq=0,[x=x2,y=y2]),
    at(eq=0,[x=x3,y=y3]),
    at(eq=0,[x=x4,y=y4]),
    at(eq=0,[x=x5,y=y5])];
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
.. and solving the system:
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
sol:solve(sys);
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
Substituting these values into the equation for the conic:
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
eqf:at(eq,first(sol));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
Here are our five points again:
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
pts;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: comment start ]
Graphing the conic section using an implicit plot:
   [wxMaxima: comment end   ] */

/* [wxMaxima: input   start ] */
load(implicit_plot);
implicit_plot(eqf=0,[x,-60,60],[y,-60,60]);
/* [wxMaxima: input   end   ] */

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