Parabolas and tools to construct them

You access the parabolas-tools by pressing the drop arrow:

[parabola_menu]

To read here you should be familiar with Generalities on tools

[parabola-characteristics]

[bullet] Parabola characterisitics

Open, one component, axis-symmetric curve of second degree, implemented as a set of points (initially 60) joined by segments. The following three construction methods make it appear always in a scheme-component. Has no anchor points but is modifiable through its masters. To draw quickly a Parabola use the vertex+focus tool. For finer drawings, the Add points tool augments the interpolation points. Corresponding symbolic constant = kParabola.

[bullet] Parabola from its vertex and focus

Menu-item: Parabola \ Parabola(vertex+focus)
Keyboard shortcut:   None
Description
Operates in two constructive stages:
In stage1(X,A), you set the vertex at A. In stage2(Y,B) you set the focus-point at B. The tool creates the parabola with these data kParabola and a scheme-component of type kParabolaAx.
Parameters
None
Remark
The points A, B are masters and changing them modifies the parabola.

[bullet] Parabola from directrix and focus

Menu-item: Parabola \ Parabola(Directrix+focus) _
Keyboard shortcut:   None
Description
Operates in two stages:
Stage1(A,B) is selective and selects at A a segment/line/side x of an object o1, whose direction will be the directrix of the parabola. Stage2(C,D) is constructive and defines at D the focus-point o2 of the parabola. The tool creates then the parabola Z with this data and a scheme component Z(o1,o2) of type kParabolaDF.
Parameters
One integer identifying the side x of o1.
Remark
The parabola is modifiable through o1 and o2(D).

[bullet] Parabola(2) through four points

Menu-item: Parabola \ Parabola through 4 pts
Keyboard shortcut:   None
Description
Operates in four constructive stages:
Stage1(X1,P1) ... stage4(X4,P4) set respectively the points at P1, ..., P4. The tool creates a group of two parabolas Z1, Z2 and a scheme component (Z1,Z2)(P1,P2,P3,P4) of type kParabola4. These are (at most two) the parabolas passing through the four points.       Picture
Parameters
Remark
For some locations of the points the parabolas can be coincident. For other locations of the four points we may have only one parabola.

Apologue, fable, poesy, and parable,
    Are false, but may be render'd also true,
By those who sow them in a land that's arable.
    'Tis wonderful what fable will not do!
'Tis said it makes reality more bearable:
    But what's reality? Who has its clue?
Philosophy? No; she too much rejects.
Religion? yes; but which of all her sects?
    Byron, Don Juan, Canto XV, 89