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Mathematics
زكريا حسناوي's user avatar
زكريا حسناوي's user avatar
زكريا حسناوي's user avatar
زكريا حسناوي
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A beautiful property of two parabolas that intersect in four points
Yes, I noticed that the property of lines passing through 4 points is true for all conic sections, but the property of the center of the circle passing through the intersections of those lines is only true for parabolas. @Semiclassical
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A beautiful property of two parabolas that intersect in four points
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A beautiful property of two parabolas that intersect in four points
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The center of gravity of a triangle on a parabola lies on the axis of symmetry
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The center of gravity of a triangle on a parabola lies on the axis of symmetry
I want to point out that I have been inspired by theorem 11.3.15 in Arseny Akopian's book
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The center of gravity of a triangle on a parabola lies on the axis of symmetry
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Find the parabola tangent to $4$ given lines
I want to point out that the parabola index required is the line connecting the points of convergence of heights of the four triangles whose sides are these lines and is called ortholine
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Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
This property is also generalized for the pole and the pole always
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Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
This property is always true for the pole and the pole.
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Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
This property is not true for the pole and the pole in general
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Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
Thank you @blue, you are right, this property is always true with respect to the electrode and the electrode, I will try to use the same idea for the rest of the properties
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Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
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Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
edited title
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Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
answered
Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
revised
Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
added 80 characters in body; edited tags
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Properties that relate to the chord of a parabola passing from the perpendicular projection of the focus point on the parabola guide
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Centers of three conical sections located on one line
I didn't expect these theorems to be so interconnected in one topic, thank you for giving me the tip of the thread to discover the interdependence of all these ideas. @brainjam
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Centers of three conical sections located on one line
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Centers of three conical sections located on one line
I would like to point out an additional note, which is that there is more than one way to choose the five points out of the ten to create a non-degenerate conic section. The centers of all of these conic sections will not lie on one line, but we will obtain different lines depending on the method of choosing the points.
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