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

/* [wxMaxima: title   start ]
Darstellung von Ellipsen,Hyperbeln
und Parabeln
   [wxMaxima: title   end   ] */

/* [wxMaxima: comment start ]
(A. Filler, Elementare Lineare Algebra, Abschnitt 2.4)
   [wxMaxima: comment end   ] */

/* [wxMaxima: section start ]
Ellipsen
   [wxMaxima: section end   ] */

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

/* [wxMaxima: input   start ] */
a: 8$
b: sqrt(48)$
e: sqrt(a^2-b^2)$
F1: [-e,0]$
F2: [e,0]$
Ellipse: x^2/a^2 + y^2/b^2 = 1;
load("draw")$
draw2d( user_preamble = ["set size ratio 1" , "set zeroaxis"], 
        ip_grid=[100,100],
        points ([F1]), points ([F2]),
        color = blue, implicit(Ellipse, x,-9,9, y,-9,9));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: subsect start ]
Darstellung von Halbellipsen als Funktionsgraphen
   [wxMaxima: subsect end   ] */

/* [wxMaxima: input   start ] */
a: 8$
b: sqrt(48)$
e: sqrt(a^2-b^2)$
F1: [-e,0]$
F2: [e,0]$
f1: b * sqrt( 1 - x^2/a^2 ) ;
f2: -b * sqrt( 1 - x^2/a^2 ) ;
load("draw")$
draw2d( user_preamble = ["set size ratio 1" , "set zeroaxis"],
        points ([F1]), points ([F2]),
        color = blue, explicit(f1, x,-a-0.5,a),
        color = black, explicit(f2, x,-a-0.5,a)
      );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Hyperbeln
   [wxMaxima: section end   ] */

/* [wxMaxima: subsect start ]
Darstellung von Hyperbeln anhand ihrer Gleichungen 
(implicit)
   [wxMaxima: subsect end   ] */

/* [wxMaxima: input   start ] */
a: 4$
b: 3$
e: sqrt(a^2-b^2)$
F1: [-e,0]$
F2: [e,0]$
Hyperbel: x^2/a^2 - y^2/b^2 = 1;
load("draw")$
draw2d( user_preamble = ["set size ratio 1" , "set zeroaxis"], 
        ip_grid=[100,100],
        points ([F1]), points ([F2]),
        color = blue, implicit(Hyperbel, x,-12,12, y,-9,9));
/* [wxMaxima: input   end   ] */

/* [wxMaxima: subsect start ]
Darstellung von Hyperbeln durch Graphen zweier Funktionen
   [wxMaxima: subsect end   ] */

/* [wxMaxima: input   start ] */
a: 4$
b: 3$
e: sqrt(a^2-b^2)$
F1: [-e,0]$
F2: [e,0]$
f1: b * sqrt(x^2/a^2 - 1) ;
f2: -b * sqrt(x^2/a^2 - 1) ;
load("draw")$
draw2d( user_preamble = ["set size ratio 1" , "set zeroaxis"],
        points ([F1]), points ([F2]),
        color = blue, explicit(f1, x,-12,12),
        color = black, explicit(f2, x,-12,12)
      );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Parabeln
   [wxMaxima: section end   ] */

/* [wxMaxima: subsect start ]
Darstellung von Parabeln (implicit)
   [wxMaxima: subsect end   ] */

/* [wxMaxima: input   start ] */
p: 3$
F: [p/2,0]$
Parabel: y^2 = 2*p*x;
Leitlinie: x=-p/2;
load("draw")$
draw2d( user_preamble = ["set size ratio 1" , "set zeroaxis"], 
        ip_grid=[100,100],
        color = red, points ([F]),
        color = blue, implicit(Parabel, x,-5,5, y,-5,5),
        color = red, implicit(Leitlinie, x,-5,5, y,-5,5) );
/* [wxMaxima: input   end   ] */

/* [wxMaxima: section start ]
Tangenten an Ellipsen
   [wxMaxima: section end   ] */

/* [wxMaxima: input   start ] */
a: 10$
b: 5$
e: sqrt(a^2-b^2)$
F1: [-e,0]$
F2: [e,0]$
tang1: -6*x/100 + 4*y/25 = 1 $
tang2: -6*x/100 - 4*y/25 = 1 $
Ellipse: x^2/a^2 + y^2/b^2 = 1;
load("draw")$
draw2d( user_preamble = ["set size ratio 1" , "set zeroaxis"], 
        ip_grid=[100,100],
        points ([F1]), points ([F2]),
        color = blue, implicit(Ellipse, x,-10.5,10.5, y,-7,7),
        color = red, implicit(tang1, x,-10.5,10.5, y,-7,7),
        color = red, implicit(tang2, x,-10.5,10.5, y,-7,7));
/* [wxMaxima: input   end   ] */

/* Maxima can't load/batch files which end with a comment! */
"Created with wxMaxima"$