# Tagged Questions

Questions on conic sections and their properties; the curves formed by the intersection of a plane and a cone. Circles, ellipses, hyperbolas, and parabolas are examples of conic sections.

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### What is the path equation that is created with the middle point of a fixed length line segment that touching both ends to an ellipse.

Ellipse equation is $(\frac{x}{a})^2+(\frac{y}{b})^2=1$ and the length of line segment is $2k$, if we move the line segment all around of the ellipse while touching both ends to the ellipse. What is ...
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### Convert ellipse parameter from General parametric form to General polar form

I am facing problem to convert ellipse standard parameters. Everything I say here is refer to http://en.wikipedia.org/wiki/Ellipse I know what are the General parametric form parameter . Lets call ...
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### How to decide that a curve segment is not an ellipse line segment?

Let me ask a question , given any short curve segment , how can you decide that it is not an ellipse line segment by a finite calculations? Thank you in advance.
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### Are two ellipse arcs always almost identical if they have the same end points and the same center of ellipses?

Edit : This question is better to be ignored until the following related question will be discussed enough. This question relates to I know "almost identical " is not mathematics. But if you have ...
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### How to find an ellipse , given 2 passing points and the tangents at them?

Please answer to a question , how to find an ellipse which passes the 2 given points and has the given tangents at them. And one related question is that the given condition can decide just one ...
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### Conics in $\mathbb{A}^2$; Hartshorne, Exercise 3.1

I'm trying to solve Exercise 3.1 in Hartshorne's Algebraic Geometry: Show that any conic in $\mathbb{A}^2$ is isomorphic to $\mathbb{A}^1$ or $\mathbb{A}^1-\{0\}$. I know from a previous ...
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### Calculate perimeter from parametric form with an ellipse?

Suppose I have a thing such as an ellipse: $$\left(\frac{x}{a}\right)^{2}+\left(\frac{y}{b}\right)^{2}=1$$ now we can define it so that $\frac{x}{a}=cos(\theta)$ and $\frac{y}{b}=sin(\theta)$. I ...
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### What is the equation of an ellipse that is not aligned with the axis?

I have the an ellipse with its semi-minor axis length $x$, and semi major axis $4x$. However, it is oriented $45$ degrees from the axis (but is still centred at the origin). I want to do some work ...
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### The Ellipse Problem - finding an ellipse inside a triangle

The problem statement is as follows: A triangle is dissected into six smaller triangles by its angle bisectors. Prove that the intersections of the angle bisectors of each of these smaller triangles ...
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### Find intersection(s) between parametrized parabola and a line

I'm trying to find the value(s) of the parameter $t$ at the intersection point(s) between a 2D general parabola (as a parametric function of $t$) and a line whose equations can be derived from two ...
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### Finding Coordinate along Ellipse Perimeter

Given an ellipse at (0, 0), with height "h" and width "w", what's the "x" coordinate along the perimeter for a given "y" coordinate?
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### How to find a generic parabola through 3 arbitrary points in R^2?

Given $(a,b)$, $(c,d)$, and $(e,f)$ (assume non-collinear and $a\neq c$, $c\neq e$, and $a\neq e$), is there a generic way to find a parabolic function between the three?
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### Ellipse: Name for the ratio $a/b$?

Given an ellipse with semi-major axis $a$ and semi-minor axis $b$, is there a "common" (or at least standard) name for either $\frac{a}{b}$ or $\frac{b}{a}$? I keep wanting to (informally) call it ...
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### Calculate intersection of two ellipses

I used the equations found here to calculate the intersection points of two circles: (P3 is what I'm trying to get) Except, now I want to do the same with two ellipses. Calculating ...
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### Finding & Plotting equation of hyperbola given foci, and difference in distances between them.

I have to plot the hyperbola (3 of them actually) in MATLAB, and so it'd be good if I could find some sort of general formula. The foci do not necessarily have to be on the axes (e.g. $(5,3)$ and ...
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### How to calculate the X Y coordinates of an ellipse with only the X and Y radius length?

I have an ellipse where the radius of x-axis = 100 and y-axis = 30. I have 3 objects where I want to evenly distribute it along the ellipse. I have already done this for a circle where both axis' ...
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### How to describe foсi of en ellipse inscribed in the triangle thru triangles angles points?

I was looking at Marden's theorem and could not help but wonder how foсi of en ellipse inscribed in the triangle can be described thru triangles angles points?
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### How to find orignal equations of type $y=ax^2+bx+c$. given 3 coordinate points?

Ok, simple question, having trouble understanding this in school. So given a set of 3 points (xy-plane), such as (40,30) (60,28) (20,25) i have to find the equation of the parabola. I ...
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### Conditions for intersection of parabolas?

What are the conditions for the existence of real solutions for the following equations: \begin{align} x^2&=a\cdot y+b\\ y^2&=c\cdot x+d\end{align} where $a,b,c,d$ are real numbers. ...
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### How do I find the equation of a tangent line to a curve?

I'm given $x^2+2x-4$ at $x=2$ and I have to find the tangent line to this curve at that point...
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### Calculating Intersection of an Ellipse and a Line

I found this page which gave me some equations on solving the intersection of a line with an ellipse given a point on the line and the slope of the line: There Isn't much explanation but ...
2k views

### How to get the limits of rotated ellipse?

The box that an ellipse fits is easily calculated if there are no rotation, or if the rotation is ${x*90^o}$ (where x is an integer) is easy. For a (major radius) and b (minor radius), it is : ...
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### Calculating Distance of a Point from an Ellipse Border

I'm thinking about using oriented ellipses to represent curves (dents/bumps etc.) in my physics engine, and have a few questions about working with them: What methods are there to finding the ...
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### Need help with the proof of conic section

Prove that the intersection of a plane and a object consist of one cone and one upside-down cone where the tip of cone meet is either degenerate conic or conic Also, idenify in what situation, the ...
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### Some question concerning curve of second order

Let $$F(x,y)=ax^2+2bxy+cy^2+2dx+2ey+f,$$ $$\phi(x,y)=ax^2+2bxy+cy^2,$$ $x,y \in \mathbb{R}$. Assume that for some $x_0, y_0 \in \mathbb{R}$ and for some $\alpha, \beta \in \mathbb{R}$ such that ...
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### Parabola with a variable starting point

I am trying to build an equation where I could start at (x,y) which are known and create a parabola from that starting point. I have no idea where it intercepts the X or Y. I know where I want the ...
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### Properties of Parabola / Optimization

I've been working through some past papers for an exam which I am due to be sitting tomorrow. In the Conic Sections paper from a couple of years ago, the following question came up: The path of a ...
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### how to find the parabola of a flying object [closed]

how can you find the parabola of a flying object without testing it? what variables do you need? I want to calculate the maximum hight and distance using a parabola. Is this possible? Any help will be ...
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### Difficult equations to rewrite as ellipses

I have this equality that defines an elliptic boundary. I am trying to rewrite it in the form of the equation of an ellipse, but I am having trouble doing that. How would I go about rewriting this ...
1k views

### Relationship between ellipsoid radii and eigenvalues

I should start by saying that I haven't done algebra for very long time. I recently have some work related to algebra, so I need some help to speedup. I went through a theorem in the book stating the ...
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### Center of gravity of an ellipse

I think the center of gravity of an ellipse is the intersection point of it's two radius. But I didn't see it anywhere, so I'm having some doubt about it. Am I right? Thanks to all.
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### Is an ellipse a circle transformed by a simple formula?

Does any ellipse $E$ have a circle $C$ such that you can obtain $E$ by transforming $C$ by a simple formula $F$? In details , both $E$ and $C$ have the same center and the axes of $E$ are the XY axes. ...
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### How to compute the cross point between an ellipse and a straight line?

Please let me know how to compute the possible cross points between an ellipse and a straight line. In details , I know the basic properties of the two shapes. So if the ellipse had its center at the ...
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### Hyperbola property

I am posting the following question under homework category. I hope I will have very good answer from mathematicians about conic sections. I have seen closely the conic sections and their ...
16k views

### Check if a point is within an ellipse

I have an ellipse centered at $(h,k)$, with semi-major axis $r_x$, semi-minor axis $r_y$, both aligned with the Cartesian plane. How do I determine if a point $(x,y)$ is within the area bounded by ...
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### an important property of an ellipse

Good morning everybody. I would like to know the proof of the following observation on the ellipse. A circle is drawn with the right latus rectum as diameter. Another circle is drawn with its ...
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### Apostol Section 13.25 #13 - Conic Sections

Question: Prove that a similarity transformation (replacing $x$ by $tx$ and $y$ by $ty$) carries an ellipse with center at the origin into another ellipse with the same eccentricity. (The next ...
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### Irreducible conic implies that the underlying matrix is invertible

I guess that it is true that a conic (2nd degree homogeneous equation in complex variables) is irreducible (i.e can't be factorized over polynomials) if and only if the underlying matrix of ...