/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
/* [ Created with wxMaxima version 0.8.5 ] */

/* [wxMaxima: title   start ]
Darstellung von Kreisen,
Lagebeziehungen zwischen Kreisen und Geraden
   [wxMaxima: title   end   ] */

/* [wxMaxima: comment start ]
(A. Filler, Elementare Lineare Algebra, Abschnitt 2.2)
   [wxMaxima: comment end   ] */

/* [wxMaxima: section start ]
Darstellung von Kreisen anhand ihrer Gleichungen 
mithilfe von draw2d-implicit
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
xM: 1.5$
yM: -1$
r: 4$
Kr1: (x-xM)^2 + (y-yM)^2 = r^2;
G1:  3*x + 4*y = -5;
load("draw")$
draw2d( user_preamble = ["set size ratio 1" , "set zeroaxis"], 
        ip_grid=[200,200],
        points ([[xM,yM]]),
        color = blue, implicit(Kr1, x,-6,6, y,-6,6),
        color = red , implicit(G1, x,-6,6, y,-6,6) );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Darstellung von Halbkreisen als Funktionsgraphen
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
xM: 1.5$
yM: -1$
r: 4$
f1: sqrt( r^2 - (x-xM)^2 ) +yM;
f2: - sqrt( r^2 - (x-xM)^2 ) +yM;
G1:  3*x + 4*y = -5;
load("draw")$
draw2d( user_preamble = ["set size ratio 1" , "set zeroaxis"],
        points ([[1.5,-1]]),
        color = blue, explicit(f1, x,xM-r,xM+r),
        color = black, explicit(f2, x,xM-r,xM+r),
        color = red , implicit(G1, x,-6,6, y,-6,6) 
      );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Lagebeziehungen Kreis-Gerade
   [wxMaxima: section end   ] */

/* [wxMaxima: subsect start ]
Darstellung eines Kreises mit einer Sekante, einer 
Tangente und einer Passante
   [wxMaxima: subsect end   ] */

/* [wxMaxima: input   start ] */
xM: 2$
yM: 3$
r: 5$
Kr1: (x-xM)^2 + (y-yM)^2 = r^2;
G1:  4*y - 3*x = 36;
G2:  4*y - 3*x = 31;
G3:  4*y - 3*x = 12;
load("draw")$
draw2d( user_preamble = ["set size ratio 1" , "set zeroaxis"], 
        ip_grid=[50,50],
        points ([[xM,yM]]),
        color = blue, implicit(Kr1, x,xM-r,xM+r, y,yM-r,yM+r),
        color = green , implicit(G1, x,-6,7, y,-2,11),
        color = red , implicit(G2, x,-6,7, y,-2,11),
        color = brown , implicit(G3, x,-6,7, y,-2,11) 
    );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: subsect start ]
Schnittpunktberechnungen
   [wxMaxima: subsect end   ] */

/* [wxMaxima: input   start ] */
solve([Kr1,G1],[x,y]), realonly:true, numer;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
solve([Kr1,G2],[x,y]), numer;
/* [wxMaxima: input   end   ] */

/* [wxMaxima: input   start ] */
solve([Kr1,G3],[x,y]), numer;
/* [wxMaxima: input   end   ] */

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