Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.

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3
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3answers
56 views

why $x^3\space +\space ax^2\space -x\space -2$ can only have one solution greater than zero

what is the proof for the above equation always having exactly one solution greater than zero for all values of a I cannot see how to prove this because you cannot factorise the polynomial and I am ...
0
votes
1answer
16 views

Find the coordinate of the point at which each straight line crosses the co-ordinate axes?

Find the coordinate of the point at which each straight line crosses the co-ordinate axes? 5x-3y = 10 is (0,10/3) the answer?
1
vote
1answer
336 views

Finding coordinates with respect to a basis

Let $B={{(1,x,x^2)}}$ and $C=(1,3x+4x^2,2x+3x^2)$ be bases for $P_2(\mathbb R)$. Find the coordinates of $x$ and $x^2$ with respect to the basis $C$. I'm a little stuck on where do begin for this ...
0
votes
1answer
103 views

equation of y=f(x) after it has been reflected in the line x=k

What is the equation of y=f(x) after it has been reflected in the line x=k For example if k=0 then it would be the y axis so the new equation would be y=f(-x) In addition what is the equation of y=f(...
0
votes
1answer
55 views

How can I get a smooth distortion on a circle with a function g(x,y)

Let's say, $$f(x,y)=x^2+y^2=1$$ gives the unit circle. Now I would like to get a smooth distortion on the circle with a function $g(x,y)$. my guess is to consider the perimeter as one dimension, so ...
3
votes
1answer
296 views

Barycentric Coordinates of the circumcenter of an arbitrary triangle

Given points $A(1, 0, 0), B(0, 1, 0), C(0, 0, 1)$ in barycentric coordinates, and points $P(x_P, y_P, z_P), Q(x_Q, y_Q, z_Q), R(x_R, y_R, z_R)$, what would the barycentric coordinates of the ...
1
vote
0answers
150 views

Convert geodetic coordinates to cartesian coordinates

I am working on some simulation software that will represent a number of entities in a defined geographic area in the world. The part of the software that I am currently working on is to implement ...
0
votes
1answer
34 views

Is it possible to write all of the functions in terms of polar form?

Is it possible to write all functions in terms of polar form? For example, the equation of the circle with radius one can be written like $r=1$ I'm wondering whether reform the equations of all curves ...
0
votes
1answer
211 views

Transformation to elliptical coordinates

I'm currently struggling to make any progress with this question. I'm a little bit thrown by the inclusion of cosh and sinh. I am aware of all of the definitions, just need guidance with approach.
1
vote
0answers
108 views

Polar coordinate system of DE's to be written in cartesian form.

Suppose we have a system in polar coordinates: $\dot r = -r$ and $\dot \theta = \frac{1}{\ln{r}}$, we are asked to solve for $r(t)$ and $\theta(t)$ explicitly, so I just integrated both equations so ...
0
votes
1answer
20 views

How is a coordinate system called where values increase to the bottom instead to the top?

In some computer graphics libraries the coordinate system is almost like the "usual" cartesian coordinate system. The only difference is that the $y$ values increas to the bottom, not to the top. ...
4
votes
1answer
232 views

Transformations from n-sphere coordinates to cartesian coordinates.

I was wondering how one would proceed to convert between coordinate systems in $ \mathbb R^n $. For $ \mathbb R^2 $ the conversion is easy and just basic trigonometry. Given $(r, \theta)$ we can ...
0
votes
1answer
310 views

Calculate X Y Z from two specific degrees on a sphere

I am a programmer, don't know much about advanced math. I would need the exact formula(s) that could achieve this, so I can translate it to my programming language. I am having a headache trying to ...
0
votes
2answers
29 views

Finding the co-ordinate vector

I can find the co-ordinate vectors for all $x$ in $R^n$ but I can't wrap my head around the ones for $x$ in $P_n$. Here is a question: Let $V$ be the space $P_3$ of all polynomials of degree at ...
0
votes
2answers
37 views

Coordinates of a vector under a basis in a Hilbert space?

Given an arbitrary basis $\{m_1, \dots, m_n \}$of a Hilbert space $H$ (or just think it as $\mathbb R^n$, and I think the methods should be the same) with given inner product, how can we find the ...
1
vote
1answer
72 views

How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$

Problem : How to find the equation of lines passing through the origin and perpendicular to the lines $xy-3y^2+y-2x+10=0$ My working on this : Two lines are perpendicular if the sum of ...
2
votes
1answer
72 views

Find the co-ordinates of the point of intersection

I have the function $$y=2x^2-3x$$ How do I find the co-ordinates of the point of intersection of the lines tangent to the curve at $y=-1$? One point where $y = -1$ is when $x = \dfrac 12$. I took ...
0
votes
1answer
28 views

Orthogonal parameterization

Consider the function $$f(a,b,c,d):=\frac{\left(a^*\right)^2b^2-\left(b^*\right)^2a^2+\left(c^*\right)^2d^2-\left(d^*\right)^2c^2}{a^*a+c^*c}$$ With complex parameters $a,b,c$ and $d$ Now find any ...
1
vote
1answer
49 views

Deal with non standard form of conic

I want to know how can I calculate latus rectum, tangent at vertex, vertex and axes of a parabola whose equation is not standard. For example, the parabola: $$ 4x^2 - 4xy + y^2 - 10 y - 19 = 0 $$
2
votes
0answers
40 views

Calculate the distance between any points in two different circles

I have two overlapping circles (C1 and C2) for which the distance between their centers is know. Inside each circle theres's random number of points (P11... P1n and P21... P2n) for which the distance ...
3
votes
3answers
508 views

Drawing a Right Triangle With Legs Not Parallel to x/y Axes?

I have been presented with an interesting problem. How can I decide whether a right triangle with given side lengths can be placed (with integer coordinate vertices) on a Cartesian plane so that the ...
0
votes
2answers
81 views

Divergence of vector in spherical coordinates

How should I calculate the divergence for $$\vec{V}=\frac {\vec{r}}{r^2}$$ Is it possible to convert it from spherical coordinates to cartesian?
2
votes
1answer
364 views

finding the coordinates of a point third of the way along a line segment

if you have a line segment and you know the coordinates of the two endpoints how do you find the coordinates of the point a third of the way along the line? In general how do find the coordinates ...
3
votes
1answer
135 views

Consider the family of lines $a(3x+4y+6)+b(x+y+2)=0$ Find the equation…

Question : Consider the family of lines $a(3x+4y+6)+b(x+y+2)=0$ Find the equation of the line of family situated at the greatest distance from the point P (2,3) Solution : The given equation can ...
1
vote
1answer
42 views

coordinate geometry high level problems

If the lines $aX^2 + 2hXY + bY^2 =0$ form two sides of a parallelogram and the line $lX + mY =1$ is one diagonal, prove that the equation of other diagonal is $Y(bl – lm) = X(am – hl)$
0
votes
1answer
50 views

What happens when this turns to $dx$?

I have this equation: $$ ds^2=c^2dt^2-dx^2-dy^2-dz^2. $$ And I've also been given $$ x=x'\cos(\Omega t)-y'\sin(\Omega t), $$ which I need to substitute into the first equation. I've squared $x$ to get ...
0
votes
0answers
95 views

Direct computation of hyperboloid-line intersection in 3d

I was wondering if a solution to this problem that doesn't involve coordinate space transformations. I have two points in 3d space, and am interested in locations where the difference of the ...
3
votes
0answers
90 views

Computing volume element in spherical coordinates

Suppose $y = (r, \theta^1, \theta^2)$ are spherical coordinates in $(\mathbb{R}^3,g)$. What is the $d\text{vol}$ in these coordinates? I solved it but I don't know if it's right. My solution: We ...
1
vote
2answers
577 views

Prove that $\mathbb{R}^\infty$ is an infinite-dimensional vector space

I am busy studying for a Linear Algebra test and came across this question in Section 4.4 of Elementary Linear Algebra (Application Version) $11^{th}$ edition. This is not part of my work that needs ...
20
votes
1answer
493 views

Infinite staircase to a circle

Suppose you start at $(0,0)$ on the unit disc and repeat the following procedure again and again: Face east and walk half-way to the circumference. Face north and walk half-way to the circumference. ...
0
votes
1answer
700 views

Convert coordinates to a different coordinate axis

Sorry for any forum rules I have broken, I needed a quick answer. I want to create a plane including 3 nonlinear points on a 3d coordinate system, one being the origin. I also need to create a ...
0
votes
3answers
285 views

Find 3rd and 4th co-ordinates for a square given co-ordinates of two points?

To construct a square we need 4 points . In my problem 2 points are given we can find 3rd and 4th point . e.g. A (1,2) B(3,5) what should be the co-ordinate of 3rd (C) and 4th (D) points . Please <...
0
votes
1answer
174 views

Using an offset data point with x, y coords to find the true centre of a circle

I have a data point at (0, 0) where measurements of a tank's shell are taken from. I have used this data point to plot the circle in a graph. However, this data point is not the true centre of the ...
2
votes
1answer
161 views

Is there an efficient way to prove orthogonality of a coordinate system?

Suppose we define a new orthogonal coordinate system, such as spherical coordinates defined by $$x = r \sin \theta \cos \phi, y = r \sin \theta \sin \phi, z = r \cos \theta.$$ Is there an efficient ...
-2
votes
1answer
29 views

$12x^2 +7xy -py^2-18x+qy+6=0$ represents a pair of $\perp$ straight lines. Find $p$ and $q$. [closed]

I'm sorry I can't show you what I've tried because I don't know how to start. For those who start from behind: p=12,q=1. Any help would be appreciated. :) thanks.
2
votes
2answers
1k views

Find the equation of the locus of a point which has its sum of distance from (0,3) and (0,-3) equal to 8.

I know the answer but due to various expressions under root, I'm unable to reach there. Is there something which I'm missing to make the solution easier? By the way the answer given is $$\frac{x^2}{...
0
votes
2answers
68 views

What is this kind of geometry called?

I want to get Cartesian coordinates of the points of a curve (e.g. a bezier curve) based on the distance (e.g length of the arc) from the start point on the curve. To make this more clear, suppose I ...
2
votes
2answers
3k views

How to rotate a vector by 90 degree?

Suppose I am given a vector in 2-D as $AB = {(x_1,y_1) ,(x_2,y_2)}$. Now , what will be the co-ordinates if I rotate the vector about the point $(x_1,y_1)$ both clockwise and counter-clockwise ?here ...
1
vote
1answer
50 views

Finding circumcenter

In a triangle A(1,2) B(2,3) C(3,1) and $\angle A = cos^{-1}(4/5)$, $\angle B = \angle C = cos^{-1}(\frac{1}{\sqrt{10} }) $ Ordinate of circumcentre of the $\triangle$ is ? I have tried solving by ...
0
votes
1answer
29 views

Find the co-ordinates of the point on the curve

Calculate the points on the curve $y=(1-x)^4$ at gradient = -4 I solve little bit $\frac{dy}{dx} = 4(1-x)^{4-1}\cdot \frac{d}{dx} (1-x)\\ = 4(1-x)^3 \cdot (-1 )$ the gradient is =-4 so I put ...
0
votes
2answers
400 views

double integral over an arbitrary triangle

Assume we have an arbitrary triangle ABC in x-y plane and we want to integrate a function $f(x,y)$ over surface of this triangle as shown in fig. 1: We can define another coordination system [x' y']...
0
votes
1answer
19 views

When to use transformation of variable and when transformation of differentials

I was reading the book: Mathematical Methods in the Physical Sciences by M. Boas and I came across this statement; I wasn't quite sure why this was the case. Is it because in the curvilinear ...
1
vote
1answer
765 views

Reaching a point B in Cartesian coordinate via Euler angles knows its initial point A Euler angles and Cartesian coordinates

I have a point A:- Known it's Cartesian coordinates (X,Y,Z) and its Euler angle Aka body rotation (R,P,Y) respectively Roll (rotation around X axis) , Pitch (rotaion around Y axis) and Yaw (rotation ...
1
vote
1answer
25 views

Find a change of coordinates matrix

Find the change of coordinates matrix that changes coordinates in the basis $1$, $1+t$ in $P_1$ to the coordinates in $1-t$, $2t$.
2
votes
4answers
131 views

locating any point on a real number line

So my question is really simple (and may be a bit naive): The claim is, I can locate any point in a 2D-plane by recursively applying the following method (possibly infinite number of times): For ...
-1
votes
2answers
51 views

Prove radius chord theorem without using congruent traingles

Suppose that $P(a,b)$ and $Q(c,d)$ are two points on the unit circle $x^2 + y^2 = 1$, and let $M$ be the midpoint of chord $PQ$. (Without using congruent triangles), prove that $OM$ is perpendicular ...
1
vote
0answers
24 views

Insert Coordinate into best place within list of coordinates in a route

I have a list of coordinates: ...
2
votes
3answers
324 views

Explanation of formula for distance between triangles in a triangular grid

Lets say you have a triangle similar to the one below, with each triangle numbered $(N, i) $ where $N$ is the row number and $i$ is the position within the row. From any triangle, you are allowed ...
0
votes
1answer
28 views

Show P, Q and R are non collinear

If P $\equiv$ $(-sin(\beta - \alpha), -cos\beta)$, Q $\equiv$ $(cos(\beta - \alpha), sin\beta)$ and R $\equiv$ $(cos(\beta - \alpha + \theta), sin(\beta - \theta))$, where $$0 \lt \alpha, \beta, \...
2
votes
3answers
231 views

How to determine if a triangle can be drawn with the given points.

Given $3$ points $$(x_1, y_1), (x_2, y_2), (x_3, y_3),$$ how does one determine whether they are vertices of a triangle? Thanks.