Parabola
Concept history
A revision trail for this concept page.
Revision 1389
8/15/2026, 3:01:28 PM · Ancient Tree
Updated text
Compare with revision 13812 changed lines
1
##### Geometric definition 2
A parabola is the set of points $M$ that are equidistant from a point $F$ called focus, and a line $D$ called directrix:2
A parabola is the set of points $M$ of the plane that are equidistant from a point $F$ called focus, and a line $D$ called directrix:3
$$\{M:MF=MH\}$$4
where $H$ is the orthogonal projection of $M$ onto $D$.5
6
```jsxgraph7
{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": false20
}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": false35
}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": false94
}95
},96
97
{98
"type": "segment",99
"parents": ["M", "H"],100
"attributes": {101
"strokeColor": "#ff4d4d",102
"strokeWidth": 2,103
"highlight": false104
}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
*Click on M and drag to visualize.*Revision 1381
8/15/2026, 2:46:13 PM · Ancient Tree
Updated text
Compare with revision 342127 changed lines
1
A parabola is...1
##### Geometric definition 2
A parabola is the set of points $M$ that are equidistant from a point $F$ called focus, and a line $D$ called directrix:3
$$\{M:MF=MH\}$$4
where $H$ is the orthogonal projection of $M$ onto $D$.5
6
```jsxgraph7
{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": false20
}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": false35
}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": false94
}95
},96
97
{98
"type": "segment",99
"parents": ["M", "H"],100
"attributes": {101
"strokeColor": "#ff4d4d",102
"strokeWidth": 2,103
"highlight": false104
}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
*Click on M and drag to visualize.*Revision 342
7/8/2026, 9:46:31 AM · Ancient Tree
Concept edited
This older revision predates detailed metadata tracking.
Revision 341
7/8/2026, 9:46:26 AM · Ancient Tree
Concept created
A parabola is...