# Tagged Questions

Questions on the use of algebraic techniques to prove geometric theorems.

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### Ellipse and parallel lines

Let's imagine that we have an ellipse described by the known equation $v^TAv=0$, (Link_1) where $v=[x \ y \ 1]^T$ (it can be a skew one in a general case). Then we have all possible parallel lines - ...
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### Find point where a line of multiple vertices overlaps itself

Since I'm not familiar with a lot of mathematical terminology, I will explain this problem with a little story. Imagine you and your friend Anne have a piece of string each, and place it on a ...
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### “A reflection across one line in the plane is, geometrically, just like a reflection across any other line.”How?

How can this statement be represented geometrically?-"A reflection across one line in the plane is, geometrically, just like a reflection across any other line." (i tried it by drawing some ...
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### Calculate Ellipse From 5 Points

How can I find a general or parametric form of equation for the ellipse having 5 points that lie within that ellipse? I have found this solution: Calculate Ellipse From Points?, where unfortunately ...
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### Affine transformations of the plane

Please help me to find the common form of affine transformations of the space $\mathbb{R}^3$ that transform the given plane $Ax + By + Cz + D = 0$ to itself. That is, all the points of this plane have ...
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### Find the value of $h$ if $x^2 + y^2 = h$

Consider equation $x^2 + y^2 = h$ that touches the line $y=3x+2$ at some point $P$. Find the value of $h$ I know that $x^2 + y^2 = h$ is a circle with radius $\sqrt{h}$. Also, since $y = 3x + 2$ ...
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### Calculus & Analytic Geometry VS Vector Calculus

This question may be applicable for Academia SE, however this is strictly math-oriented and requires math whizzes' opinions. I intend to go to a tech institute to get a BS majoring in Computer ...
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### Show that the vertex lies on the surface $z^2(\frac{x}{a}+\frac{y}{b})=4(x^2+y^2)$

Two cones with a common vertex pass through the curves $z^2=4ax,y=0$ and $z^2=4by,x=0.$ The plane $z=0$ meets them in two conics which intersect in four concyclic points.Show that the vertex lies on ...
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### Two points are given as A(2,0) and B(8,0). What's the value of y (y>0), so that C(0,y) is such that angle ACB has maximum value?

My first guess is that it could be found as first derivative of some function, but I don't have idea what that function could be.
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### Distance of closest aproach [closed]

A particle is kept at rest at origin. Another particle starts from $(5,0)$ with a velocity of $-4i+3j$. Find the closest distance of approach.
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### What are the coordinates of the intersection points of two circles?

You have 2 circles that intersect in 2 points. You know the coordinates of their centers and you also know their radius. My question is: What are the coordinates of these 2 intersection points?
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### Oblate Spheroidal Coordinates, Confocal Ellipsoidal Coordinates and Geodesy

What is the name of the orthogonal coordinate system that is most commonly used in modern geodesy\geomatics engineering to model the reference ellipsoid? I suspect it is either oblate spheroidal ...
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### Projection of vectors over along their axis

I have difficulties to understand first how does the strong blue vectors appear Second, how does the light blue vector $w=u\times v$ appears? I thought it was going to be $\vec 0$
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### Projection of a point on a line

Find the projection of the point $(-6,4)$ onto the line $4x-5y+3=0$ I can find the distance between the point and the line, but I do not think it can help
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### Properties of polyhedron solving constrained max problem

This is a question for people who don't have trouble to think in more than two dimensions. Don't hesitate to ask clarifying questions! Let us suppose we have $n$ random variables $X_i$ that are iid ...