Questions tagged [conic-sections]
For questions about circles, ellipses, hyperbolas, and parabolas. These curves are the result of intersecting a cone with a plane.
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polarization ellipse for complex eigenvalues corresponding the phase and eigenstates. [closed]
I want to draw polarization ellipses at 0.0 eV, 0.12 eV, 0.16 eV, and 0.2 eV for my transmission eigen-polarization-values plots using eigenphase data (in radians). I've attached the final result ...
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Least Squares Ellipse with known parameters
Given a set of points in 2D space
$$P = \{(x_i, y_i), \text{for } i \text{ in }1 \dots N\}$$
I want to find the least squares fit of an ellipse
$$\frac{(x - c_x)^2}{r_x^2} + \frac{(y - c_y)^2}{r_y^2} =...
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A beautiful property of two parabolas that intersect in four points
I have just come up with a very cool property of two parabolas intersecting at four points, I want to know whether this property is already known or not and how to prove it.
We have two parabolas ...
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Locus of a point whose distance from two points is fixed (but not necessarily equal) in 3D geometry
Suppose there are two fixed points $S_1$ and $S_2$
Let the moving point be $P$
$PS_1$ and $PS_2$ are fixed but not necessarily equal.
Now I think it is a circle. Obtained by rotation of vertex of ...
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Elliptical Grid Mapping in Shader
I wanted to make a Elliptical Grid Mapping Shader, but it is not a perfect square and it is rotated.
If i multiply the coords by sqrt(2.) and divides them after again, it is an square, but still ...
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The center of gravity of a triangle on a parabola lies on the axis of symmetry
About an hour ago, I discovered a beautiful property of a parabola.
If a circle intersects a parabola at four points, one of which is the vertex of the parabola, then the center of the triangle, ...
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Double Contact Chained Ellipses Problem
A few years ago, when I played around with GeoGebra, I came up with the following conjecture.
Conjecture
Let $n\in\mathbb{N}, n\geq3$. Let $E$ be an ellipse, and let $E_{1}, E_{2}, \dots, E_{n}$ be ...
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Largest Area Triangle in the Vesica Piscis
I can place any three points in or on a vesica piscis1. I wish to find the triangle of maximum area. I know the area of the vesica piscis is $(\frac{2π}{3}-\frac{\sqrt{3}}{2})d^2$ (where d is the ...
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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 [closed]
Now I remembered
my previous question about finding the harmonic mean using a parabola and my answer, which included a second method. That second method inspired me to try more in this configuration ...
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Line tangent to a parabola
So I was doing some AoPS Alcumus and came across this problem with a weird solution. A quadratic function $p(x)$ has lines of tangency $y=-11x-37$, $y=x-1$, and $y=9x+3$. These lines are tangent to $p$...
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Complete specification of the intersection between an elliptical cone and a plane [closed]
Suppose you're given the elliptical cone
$ (z - h)^2 = \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} $
And the plane $ N \cdot r = d $ where $r = (x,y,z) $. Assume that $N$ is such that the intersection ...
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Construct a cone from independently sampled surface points
2 points are sufficient to determine a 3D line, 3 points are sufficient to determine a 3D plane and there are well-known formulas to construct lines and planes from such points.
I understand that ...
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Golden ratio points in ellipse
This is a property of the ellipse. The sum of distances to the foci is constant:
In particular, some of these points must satisfy the golden ratio relationship:
Given the equation of the ellipse in ...
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Largest Elliptic Cone Intersecting with Sphere
I have a function that can be reasonably approximated with an elliptic cone with a certain excentricity I can calculate, I have the dimensions of the axes so for example a = 1 and b = 0.25.
I then ...
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Parametric eqn of an ellipse and the meaning of the angle "t"
I don't understand what the angle "t" is in the parametric equation of an ellipse.
The parametric equation from books is given as:
$$x = a\cos t$$
$$y = b\sin t$$
Referring to the diagram, ...
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