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Improve hyperbola image
I hate to complain when someone puts a lot of work into creating images, but it would be nice if the image of the hyperbola made it visually apparent that a hyperbola has two asymptotes. (A common error committed by students asked to draw graphs showing the asymptotes is to draw the lines in the right places and then draw a curve that does not at all appear to approach the lines; a good image could help them understand that that is an error.) Michael Hardy21:23, 17 May 2003 (UTC)[reply]
I came here to point out that the picture of the hyperbola does not appear to be very hyperbolic; then I saw that Michael Hardy had a similar complaint. Is that picture really a hyperbola? Dominus02:44, 12 June 2003 (UTC)[reply]
Observations about two more figures.
In the figure Conic parameters in the case of an ellipse,
distances on my screen were as follows.
300 mm from left focus to end of minor axis
35 mm from left focus to left end of major axis
78 mm from left directrix to left end of maror axis.
Ratio: 0.45
567 mm from left focus to right end of the major axis
675 mm from left directrix to right end ot major axis.
Ratio 0.84
The two ratios should be equal!
The image above it is titled
Circle (e=0), ellipse (e=1/2), parabola (e=1) and hyperbola (e=2) with fixed focus F and directrix (e=∞)
and it shows a circle with radius 10 mm and directrix 44 mm from the center. According to my calculation, the excentricity of this circle is 0.23 but it is also stated that for this circle, e is not only 0, it is also infinite. — Preceding unsigned comment added by Peterungar (talk • contribs) 18:51, 25 October 2020 (UTC)[reply]
I don't know what you are measuring, but the eccentricity of a circle is defined to be zero and no measurement is going to verify that. The eccentricity of a line is infinite, which follows from this definition. --Bill Cherowitzo (talk) 20:55, 25 October 2020 (UTC)[reply]
Perhaps you were misled by the caption, which I have corrected. The circle does not have a directrix (in the Euclidean plane) and the old caption implied that it did. --Bill Cherowitzo (talk) 19:54, 26 October 2020 (UTC)[reply]
Edit request to Conics Intersection paragraph, 29 November 2010
{{edit semi-protected}}
Please add the reference to this MATLAB Central URL containing the code to detect conics intersection:
The three types of conic section are the hyperbola, the parabola, and the ellipse.
This is incomplete as there are in fact six conic section. If the tip of the cone is part of the intersection, you get either a point, a line or a pair of intersecting lines. --2003:C1:4F43:D266:9C32:E257:E615:42C8 (talk) 18:22, 14 January 2021 (UTC)[reply]
Semi-protected edit request on 4 February 2021 to update types of conic sections image
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Types of conic sections: 1. Circle 2. Ellipse 3. Parabola 4. Hyperbola 5. Line (not included) 6. Point (not included)
1. Replace current image for types of conic sections with this one.
2. Possibly update description in order to account for all types of conic sections.
Benefits are I separated items circle and ellipse for ease of understanding, also all visualization was done in model to remove artifacts of human error such as incorrect layering and intersect lines that lead to incorrect intuition. JensVyff (talk) 23:03, 4 February 2021 (UTC)[reply]
@JensVyff: Thanks for creating a new visualization! I'd say that splitting circle and ellipse was the right call. I've formatted the image to the left to show what it would look like in the article. I would make the ellipse plane more "slanted" to exaggerate the difference between the circle. Also, could you get rid of some of the white space? The four pictures can be closer together, and get rid of some of the extra margins too. ◢ Ganbaruby! (Say hi!) 00:19, 5 February 2021 (UTC)[reply]
I agree with Ganbaruby's suggestion. Moreover, the caption must be improved by: 1. removing the cases of a line and a point (there are not conic sections in the sense of the article); 2. adding {{nowrap}} templates and semicolons for avoiding confusing line breaks. Here would be the source of the resulting caption: Types of conic sections: {{nowrap|1: Circle;}} {{nowrap|2: Ellipse;}} {{nowrap|3: Parabola;}} {{nowrap|4: Hyperbola}}. D.Lazard (talk) 11:23, 5 February 2021 (UTC)[reply]
Great suggestions. Let me know what you think of the update. The description definately needed some formatting, but I reverted the description back to previous style and kept the hyperlink formatting. I am unsure if the nowraps are required on such short lines.Types of conic sections: 1: Circle 2: Ellipse 3: Parabola 4: HyperbolaJensVyff (talk) 02:21, 6 February 2021 (UTC)[reply]
I have changed the figure in the article, with the format of the caption changed (3 lines instead of 5). I have used non-breacking spaces for column alignment, but I am not sure that this work well on every device. If not, it is easy to change it (in any case, easier than changing the figure itself). D.Lazard (talk) 09:39, 6 February 2021 (UTC)[reply]
Type of conic for given equation ax^2+bxy+cy^2+dx+ey+f=0
For ax^2+bxy+cy^2+dx+ey+f=0:
Let D=b^2-4ac and Q=det(a,b/2,d/2;b/2,c,e/2;d/2,e/2,f) and R=d^2+e^2-4(a+c)f
This is hardly human readable, and seems almost correct (the case is ommitted). In any case this classification is given in § Discriminant for the case (true conics), with a link to Degenerate conic § Discriminant for the degenerate cases. Maybe, the complete classification should be made more visible, but your style is definitively not convenient for Wikipedia. D.Lazard (talk) 15:30, 11 September 2021 (UTC)[reply]
Some psychological tests use the similar thing, the correct thing should be:
For ax^2+bxy+cy^2+dx+ey+f=0:
Let D=b^2-4ac and Q=det(a,b/2,d/2;b/2,c,e/2;d/2,e/2,f) and R=d^2+e^2-4(a+c)f
1.
D>0 --> goto 2
D=0 --> goto 3
D<0 --> goto 4
2.
Q=0 --> (two intersecting straight lines)
Q≠0 --> (hyperbola)
3.
Q=0 --> goto 5
Q≠0 --> (parabola)
4.
Q=0 --> (a single point)
Q≠0 --> goto 6
5.
a=0 and b=0 and c=0 --> goto 7
a≠0 and/or b≠0 and/or c≠0 --> goto 8
