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Please add the reference to this MATLAB Central URL containing the code to detect conics intersection:
http://www.mathworks.com/matlabcentral/fileexchange/28318-conics-intersection
Pierluigi ( talk) 8:52, 29 November 2010 (UTC)
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 lines) Q≠0 --> (hyperbola)
3.
Q=0 --> goto 5 Q≠0 --> (parabola)
4.
Q=0 --> (a single point) Q≠0 --> goto 6
5.
R>0 --> (two parallel straight lines) R=0 --> (a single line) R<0 --> (empty set)
6.
(a+c)Q>0 --> (empty set) (a+c)Q<0 --> goto 7
7.
a=c and b=0 --> (circle) a≠c and/or b≠0 --> (ellipse)
Is it right? 2402:7500:92E:A23D:349B:A9A7:2AAF:1C1E ( talk) 12:53, 11 September 2021 (UTC)
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
6.
(a+c)Q>0 --> (empty set)
(a+c)Q<0 --> goto 9
7.
d=0 and e=0 --> goto 10
d≠0 and/or e≠0 --> (a single straight line)
8.
R>0 --> (two parallel straight lines)
R=0 --> (a single straight line)
R<0 --> (empty set)
9.
a=c and b=0 --> (circle)
a≠c and/or b≠0 --> (ellipse)
10.
f=0 --> (the full plane)
f≠0 --> (empty set)
Note: In step 6, (a+c)Q cannot be =0, since D<0, and D<0 implies ac>0, thus a+c cannot be =0 since a and c are real numbers, also Q is not 0
114.41.119.57 ( talk) 09:13, 12 September 2021 (UTC)
What does it mean? Term not used in article. Equinox ◑ 23:15, 24 October 2022 (UTC)
"The latus rectum is the chord parallel to the directrix and passing through a focus; its half-length is the semi-latus rectum (ℓ)."– jacobolus (t) 00:24, 25 October 2022 (UTC)
This
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change "ooooooo" to "usually" in the section "intersection at infinity" Atobi16 ( talk) 10:57, 25 November 2022 (UTC)
"oooooooo" removed. D.Lazard ( talk) 12:37, 25 November 2022 (UTC)
It did confuse me, anyway. It starts with :
> In homogeneous coordinates a conic section can be represented as:
But that is the equation of a surface, not a curve. In fact, if I'm not mistaken it's the equation of the cone of whom the conic is a section with a plan. It's easy to see when we notice that the matrix is symmetric and thus can be diagonalized by an orthogonal matrix, with real eigenvalues. Necessarily at least one eigenvalue is negative (otherwise we have a sphere of nul radius, that is just a point), and we have the equation of a cone.
I think this ought to be clarified. Grondilu ( talk) 05:37, 22 December 2022 (UTC)
This
level-4 vital article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
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This page has archives. Sections older than 365 days may be automatically archived by Lowercase sigmabot III when more than 5 sections are present. |
{{edit semi-protected}}
Please add the reference to this MATLAB Central URL containing the code to detect conics intersection:
http://www.mathworks.com/matlabcentral/fileexchange/28318-conics-intersection
Pierluigi ( talk) 8:52, 29 November 2010 (UTC)
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 lines) Q≠0 --> (hyperbola)
3.
Q=0 --> goto 5 Q≠0 --> (parabola)
4.
Q=0 --> (a single point) Q≠0 --> goto 6
5.
R>0 --> (two parallel straight lines) R=0 --> (a single line) R<0 --> (empty set)
6.
(a+c)Q>0 --> (empty set) (a+c)Q<0 --> goto 7
7.
a=c and b=0 --> (circle) a≠c and/or b≠0 --> (ellipse)
Is it right? 2402:7500:92E:A23D:349B:A9A7:2AAF:1C1E ( talk) 12:53, 11 September 2021 (UTC)
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
6.
(a+c)Q>0 --> (empty set)
(a+c)Q<0 --> goto 9
7.
d=0 and e=0 --> goto 10
d≠0 and/or e≠0 --> (a single straight line)
8.
R>0 --> (two parallel straight lines)
R=0 --> (a single straight line)
R<0 --> (empty set)
9.
a=c and b=0 --> (circle)
a≠c and/or b≠0 --> (ellipse)
10.
f=0 --> (the full plane)
f≠0 --> (empty set)
Note: In step 6, (a+c)Q cannot be =0, since D<0, and D<0 implies ac>0, thus a+c cannot be =0 since a and c are real numbers, also Q is not 0
114.41.119.57 ( talk) 09:13, 12 September 2021 (UTC)
What does it mean? Term not used in article. Equinox ◑ 23:15, 24 October 2022 (UTC)
"The latus rectum is the chord parallel to the directrix and passing through a focus; its half-length is the semi-latus rectum (ℓ)."– jacobolus (t) 00:24, 25 October 2022 (UTC)
This
edit request has been answered. Set the |answered= or |ans= parameter to no to reactivate your request. |
change "ooooooo" to "usually" in the section "intersection at infinity" Atobi16 ( talk) 10:57, 25 November 2022 (UTC)
"oooooooo" removed. D.Lazard ( talk) 12:37, 25 November 2022 (UTC)
It did confuse me, anyway. It starts with :
> In homogeneous coordinates a conic section can be represented as:
But that is the equation of a surface, not a curve. In fact, if I'm not mistaken it's the equation of the cone of whom the conic is a section with a plan. It's easy to see when we notice that the matrix is symmetric and thus can be diagonalized by an orthogonal matrix, with real eigenvalues. Necessarily at least one eigenvalue is negative (otherwise we have a sphere of nul radius, that is just a point), and we have the equation of a cone.
I think this ought to be clarified. Grondilu ( talk) 05:37, 22 December 2022 (UTC)