# Tagged Questions

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

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 ...
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?
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 ...
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(...
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 ...
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 ...
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 ...
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 ...
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.
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 ...
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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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: $$4x^2 - 4xy + y^2 - 10 y - 19 = 0$$
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 ...
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 ...
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?
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 ...
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 ...
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 $Y(bl – lm) = X(am – hl)$
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 ...
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 ...
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 ...
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 ...
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. ...
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 ...
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 <...
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 ...
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 ...
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.
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}{... 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 ... 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 ... 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 ... 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 ... 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']... 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 ... 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 ... 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. 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 ... 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 ... 0answers 24 views ### Insert Coordinate into best place within list of coordinates in a route I have a list of coordinates: ... 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 ... 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, \...
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.