Ivan Shishkin, Birch Grove

Parabole

Concept history

A revision trail for this concept page.

5 revisions

Back

Revision 3067

8/30/2026, 9:10:04 PM · araucaria araucana

à propos de la directrice : point D -> droite D

Compare with revision 14212 changed lines
1##### Définition géométrique
2Une parabole est l'ensemble des points $M$ du plan à équidistance d'un point $F$ appelé foyer, et d'un point $D$ appelé directrice :
2Une parabole est l'ensemble des points $M$ du plan à équidistance d'un point $F$ appelé foyer, et d'une droite $D$ appelé directrice :
3$$\{M:MF=MH\}$$
4où $H$ est la projection orthogonale de $M$ sur $D$.
5
6```jsxgraph
7{
8 "boundingBox": [-5, 5.5, 5, -2],
9 "axis": false,
10 "height": 520,
11 "elements": [
12 {
13 "id": "parabola",
14 "type": "functiongraph",
15 "parents": ["x^2/4", -4.5, 4.5],
16 "attributes": {
17 "strokeColor": "#24b6f0",
18 "strokeWidth": 2,
19 "highlight": false
20 }
21 },
22
23 {
24 "id": "D",
25 "type": "line",
26 "parents": [[-5, -1], [5, -1]],
27 "attributes": {
28 "strokeColor": "#333333",
29 "strokeWidth": 2,
30 "straightFirst": false,
31 "straightLast": false,
32 "fixed": true,
33 "highlight": false,
34 "withLabel": false
35 }
36 },
37
38 {
39 "id": "F",
40 "type": "point",
41 "parents": [0, 1],
42 "attributes": {
43 "name": "F",
44 "size": 3,
45 "fixed": true,
46 "fillColor": "#333333",
47 "strokeColor": "#333333",
48 "highlight": false,
49 "label": {
50 "offset": [10, 10]
51 }
52 }
53 },
54
55 {
56 "id": "M",
57 "type": "glider",
58 "parents": [2.8, 1.96, "parabola"],
59 "attributes": {
60 "name": "M",
61 "size": 3,
62 "fillColor": "#ff4d4d",
63 "strokeColor": "#ff4d4d",
64 "label": {
65 "offset": [10, 10]
66 }
67 }
68 },
69
70 {
71 "id": "H",
72 "type": "point",
73 "parents": ["M.X()", -1],
74 "attributes": {
75 "name": "H",
76 "size": 2,
77 "fixed": true,
78 "fillColor": "#333333",
79 "strokeColor": "#333333",
80 "highlight": false,
81 "label": {
82 "offset": [10, -18]
83 }
84 }
85 },
86
87 {
88 "type": "segment",
89 "parents": ["M", "F"],
90 "attributes": {
91 "strokeColor": "#ff4d4d",
92 "strokeWidth": 2,
93 "highlight": false
94 }
95 },
96
97 {
98 "type": "segment",
99 "parents": ["M", "H"],
100 "attributes": {
101 "strokeColor": "#ff4d4d",
102 "strokeWidth": 2,
103 "highlight": false
104 }
105 },
106
107 {
108 "id": "Dlabel",
109 "type": "point",
110 "parents": [4.15, -0.75],
111 "attributes": {
112 "name": "D",
113 "size": 0,
114 "fixed": true,
115 "strokeOpacity": 0,
116 "fillOpacity": 0,
117 "highlight": false,
118 "label": {
119 "offset": [0, 0]
120 }
121 }
122 }
123 ]
124}
125```
126*Cliquer sur M et tirer pour visualiser.*

Revision 1421

8/15/2026, 7:18:27 PM · Ancient Tree

Translation marked up to date

translation freshnessSource revision 1381Source revision 1389

Revision 1388

8/15/2026, 3:00:54 PM · Ancient Tree

Updated text

Compare with revision 13872 changed lines
1##### Définition géométrique
2Une parabole est l'ensemble des points $M$ à équidistance d'un point $F$ appelé foyer, et d'un point $D$ appelé directrice :
2Une parabole est l'ensemble des points $M$ du plan à équidistance d'un point $F$ appelé foyer, et d'un point $D$ appelé directrice :
3$$\{M:MF=MH\}$$
4où $H$ est la projection orthogonale de $M$ sur $D$.
5
6```jsxgraph
7{
8 "boundingBox": [-5, 5.5, 5, -2],
9 "axis": false,
10 "height": 520,
11 "elements": [
12 {
13 "id": "parabola",
14 "type": "functiongraph",
15 "parents": ["x^2/4", -4.5, 4.5],
16 "attributes": {
17 "strokeColor": "#24b6f0",
18 "strokeWidth": 2,
19 "highlight": false
20 }
21 },
22
23 {
24 "id": "D",
25 "type": "line",
26 "parents": [[-5, -1], [5, -1]],
27 "attributes": {
28 "strokeColor": "#333333",
29 "strokeWidth": 2,
30 "straightFirst": false,
31 "straightLast": false,
32 "fixed": true,
33 "highlight": false,
34 "withLabel": false
35 }
36 },
37
38 {
39 "id": "F",
40 "type": "point",
41 "parents": [0, 1],
42 "attributes": {
43 "name": "F",
44 "size": 3,
45 "fixed": true,
46 "fillColor": "#333333",
47 "strokeColor": "#333333",
48 "highlight": false,
49 "label": {
50 "offset": [10, 10]
51 }
52 }
53 },
54
55 {
56 "id": "M",
57 "type": "glider",
58 "parents": [2.8, 1.96, "parabola"],
59 "attributes": {
60 "name": "M",
61 "size": 3,
62 "fillColor": "#ff4d4d",
63 "strokeColor": "#ff4d4d",
64 "label": {
65 "offset": [10, 10]
66 }
67 }
68 },
69
70 {
71 "id": "H",
72 "type": "point",
73 "parents": ["M.X()", -1],
74 "attributes": {
75 "name": "H",
76 "size": 2,
77 "fixed": true,
78 "fillColor": "#333333",
79 "strokeColor": "#333333",
80 "highlight": false,
81 "label": {
82 "offset": [10, -18]
83 }
84 }
85 },
86
87 {
88 "type": "segment",
89 "parents": ["M", "F"],
90 "attributes": {
91 "strokeColor": "#ff4d4d",
92 "strokeWidth": 2,
93 "highlight": false
94 }
95 },
96
97 {
98 "type": "segment",
99 "parents": ["M", "H"],
100 "attributes": {
101 "strokeColor": "#ff4d4d",
102 "strokeWidth": 2,
103 "highlight": false
104 }
105 },
106
107 {
108 "id": "Dlabel",
109 "type": "point",
110 "parents": [4.15, -0.75],
111 "attributes": {
112 "name": "D",
113 "size": 0,
114 "fixed": true,
115 "strokeOpacity": 0,
116 "fillOpacity": 0,
117 "highlight": false,
118 "label": {
119 "offset": [0, 0]
120 }
121 }
122 }
123 ]
124}
125```
126*Cliquer sur M et tirer pour visualiser.*

Revision 1387

8/15/2026, 2:58:41 PM · Ancient Tree

Updated text

Compare with revision 13862 changed lines
1##### Définition géométrique
2Une parabole est l'ensemble des points $M$ à équidistance d'un point $F$ appelé foyer, et d'un point $D$ appelée directrice :
2Une parabole est l'ensemble des points $M$ à équidistance d'un point $F$ appelé foyer, et d'un point $D$ appelé directrice :
3$$\{M:MF=MH\}$$
4où $H$ est la projection orthogonale de $M$ sur $D$.
5
6```jsxgraph
7{
8 "boundingBox": [-5, 5.5, 5, -2],
9 "axis": false,
10 "height": 520,
11 "elements": [
12 {
13 "id": "parabola",
14 "type": "functiongraph",
15 "parents": ["x^2/4", -4.5, 4.5],
16 "attributes": {
17 "strokeColor": "#24b6f0",
18 "strokeWidth": 2,
19 "highlight": false
20 }
21 },
22
23 {
24 "id": "D",
25 "type": "line",
26 "parents": [[-5, -1], [5, -1]],
27 "attributes": {
28 "strokeColor": "#333333",
29 "strokeWidth": 2,
30 "straightFirst": false,
31 "straightLast": false,
32 "fixed": true,
33 "highlight": false,
34 "withLabel": false
35 }
36 },
37
38 {
39 "id": "F",
40 "type": "point",
41 "parents": [0, 1],
42 "attributes": {
43 "name": "F",
44 "size": 3,
45 "fixed": true,
46 "fillColor": "#333333",
47 "strokeColor": "#333333",
48 "highlight": false,
49 "label": {
50 "offset": [10, 10]
51 }
52 }
53 },
54
55 {
56 "id": "M",
57 "type": "glider",
58 "parents": [2.8, 1.96, "parabola"],
59 "attributes": {
60 "name": "M",
61 "size": 3,
62 "fillColor": "#ff4d4d",
63 "strokeColor": "#ff4d4d",
64 "label": {
65 "offset": [10, 10]
66 }
67 }
68 },
69
70 {
71 "id": "H",
72 "type": "point",
73 "parents": ["M.X()", -1],
74 "attributes": {
75 "name": "H",
76 "size": 2,
77 "fixed": true,
78 "fillColor": "#333333",
79 "strokeColor": "#333333",
80 "highlight": false,
81 "label": {
82 "offset": [10, -18]
83 }
84 }
85 },
86
87 {
88 "type": "segment",
89 "parents": ["M", "F"],
90 "attributes": {
91 "strokeColor": "#ff4d4d",
92 "strokeWidth": 2,
93 "highlight": false
94 }
95 },
96
97 {
98 "type": "segment",
99 "parents": ["M", "H"],
100 "attributes": {
101 "strokeColor": "#ff4d4d",
102 "strokeWidth": 2,
103 "highlight": false
104 }
105 },
106
107 {
108 "id": "Dlabel",
109 "type": "point",
110 "parents": [4.15, -0.75],
111 "attributes": {
112 "name": "D",
113 "size": 0,
114 "fixed": true,
115 "strokeOpacity": 0,
116 "fillOpacity": 0,
117 "highlight": false,
118 "label": {
119 "offset": [0, 0]
120 }
121 }
122 }
123 ]
124}
125```
126*Cliquer sur M et tirer pour visualiser.*

Revision 1386

8/15/2026, 2:58:02 PM · Ancient Tree

Concept created

##### Définition géométrique 
Une parabole est l'ensemble des points $M$ à équidistance d'un point $F$ appelé foyer, et d'un point $D$ appelée directrice :
$$\{M:MF=MH\}$$
où $H$ est la projection orthogonale de $M$ sur $D$.

```jsxgraph
{
  "boundingBox": [-5, 5.5, 5, -2],
  "axis": false,
  "height": 520,
  "elements": [
    {
      "id": "parabola",
      "type": "functiongraph",
      "parents": ["x^2/4", -4.5, 4.5],
      "attributes": {
        "strokeColor": "#24b6f0",
        "strokeWidth": 2,
        "highlight": false
      }
    },

    {
      "id": "D",
      "type": "line",
      "parents": [[-5, -1], [5, -1]],
      "attributes": {
        "strokeColor": "#333333",
        "strokeWidth": 2,
        "straightFirst": false,
        "straightLast": false,
        "fixed": true,
        "highlight": false,
        "withLabel": false
      }
    },

    {
      "id": "F",
      "type": "point",
      "parents": [0, 1],
      "attributes": {
        "name": "F",
        "size": 3,
        "fixed": true,
        "fillColor": "#333333",
        "strokeColor": "#333333",
        "highlight": false,
        "label": {
          "offset": [10, 10]
        }
      }
    },

    {
      "id": "M",
      "type": "glider",
      "parents": [2.8, 1.96, "parabola"],
      "attributes": {
        "name": "M",
        "size": 3,
        "fillColor": "#ff4d4d",
        "strokeColor": "#ff4d4d",
        "label": {
          "offset": [10, 10]
        }
      }
    },

    {
      "id": "H",
      "type": "point",
      "parents": ["M.X()", -1],
      "attributes": {
        "name": "H",
        "size": 2,
        "fixed": true,
        "fillColor": "#333333",
        "strokeColor": "#333333",
        "highlight": false,
        "label": {
          "offset": [10, -18]
        }
      }
    },

    {
      "type": "segment",
      "parents": ["M", "F"],
      "attributes": {
        "strokeColor": "#ff4d4d",
        "strokeWidth": 2,
        "highlight": false
      }
    },

    {
      "type": "segment",
      "parents": ["M", "H"],
      "attributes": {
        "strokeColor": "#ff4d4d",
        "strokeWidth": 2,
        "highlight": false
      }
    },

    {
      "id": "Dlabel",
      "type": "point",
      "parents": [4.15, -0.75],
      "attributes": {
        "name": "D",
        "size": 0,
        "fixed": true,
        "strokeOpacity": 0,
        "fillOpacity": 0,
        "highlight": false,
        "label": {
          "offset": [0, 0]
        }
      }
    }
  ]
}
```
*Cliquer sur M et tirer pour visualiser.*