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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5
votes
2answers
144 views

Cylindrical coordinates on elliptic paraboloids.

I want to compute the volume bounded by: the cylinder $x^2+4y^2=4$. the $z=0$ plane. the elliptic paraboloid $z = x^2 + 6y^2$. I would like to use cylindrical coordinates. However I have never ...
0
votes
1answer
14 views

Co-ordinate vector of the linear transformation of x

$T$ is the linear transformation of $V$ ($n$-dimensional) to $W$ ($m$-dimensional) and {$b_1,...b_n$} is the basis $B$ for $V.$ Given any x in $V$, the coordinate vector $[x]_B$ is in $R^n$ and the ...
2
votes
4answers
95 views

How to find coordinates of reflected point?

How can I find the coordinates of a point reflected over a line that may not necessarily be any of the axis? Example Question: If P is a reflection (image) of point (3, -3) in the line $2y = ...
0
votes
3answers
43 views

$x^2+y^2=5$ and point $(-4,3)$. Find the equations of the tangents to the circle and the point.

$x^2+y^2=5^2$ and point $(-4,3)$. Find the equations of the tangents to the circle and the point. This question came up in class and we were unsure of how to do it. Our class spent a good 20 minutes ...
0
votes
0answers
29 views

Co-ordinate chart and components of a vector field.

Q) Using a coordinate chart, give a formula for the components of the vector field $[v,w]$ in terms of the components of $v$ and $w$. Where $[v,w]: f \mapsto v(wf) - w(vf)$ I don't know what the ...
1
vote
0answers
44 views

Determine third point of triangle when two points and all sides are known

I am solving basically the same problem as asked in this thread Determine third point of triangle when two points and all sides are known? I know 3 sides of a triangle and positions of two of them. ...
0
votes
1answer
13 views

Number of straight line through point forming same area with axes

I am given a point $P(2,3)$ thru which passing line forms triangle with axes of area $12$ , so how many lines will pass thru $P$ making same area with axes? Writing intercept form of line ...
0
votes
0answers
8 views

Rotate a point on circle by an angle such that the point attains a new coordinate axis.

I have this circle with known radius and centre w.r.t to both new and old coordinate axes given by NBase and Base respectively. I need to find a point P and Theta such that when vector OP is rotated ...
0
votes
1answer
14 views

Linear mapping coordinate question - need help

I am given the set $B=[(2,3),(1,2)]$ and $C=[(2,1),(1,1)]$. $L: \mathbb R^2\to \mathbb R^2$ is the linear mapping such that $[x]_B = [L(x)]_C$ (like coordinate vector stuff). I am told to find ...
3
votes
3answers
53 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
12 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
53 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
16 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 ...
0
votes
1answer
30 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 ...
2
votes
1answer
43 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
17 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
25 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
23 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.
0
votes
0answers
27 views

Finding a way between two points

Let's assume we have two points $A(x_1,y_1)$ and $B(x_2,y_2)$ in 2-D space. And we need to find a trajectory for going from one point to the other. But the problem is that in this space prohibiting ...
1
vote
0answers
54 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
0answers
20 views

Jacobian equals the product of scale factors

I have to prove that in 2 dimensions $J(\frac{x,y}{q_1,q_2})=h_1 h_2$ (1), where $q_1, q_2$ are the new mutually perpendicular coordinates and $h_1, h_2$ are the respective scale factors (exercise ...
0
votes
1answer
16 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. ...
2
votes
1answer
26 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
42 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
0answers
27 views

How to check if a set of coordinates creates a polygon?

Well, hello. I've got a set of coordinates and i want to check if it creates one polygon or 2 (or more) polygons. Coordinates are being read from input stream, one after another, for example: ...
0
votes
2answers
20 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
23 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 ...
0
votes
1answer
29 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 ...
0
votes
2answers
31 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
25 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 ...
0
votes
1answer
23 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
26 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 ...
0
votes
0answers
17 views

Cordinate geometry problem

The base of a triangle passes through fixed point $(1,1)$ and its sides are bisected at right angle by the lines $y^2 - 8xy - 9x^2 =0$. If the locus of its vertex is a circle of radius ${(k/2)}^{1/2} ...
3
votes
3answers
203 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
26 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?
0
votes
0answers
17 views

Why is the Laplace/Helmholtz equation only separable in a finite number of coordinate systems?

On MathWorld one finds that the Helmholtz equation $$(\nabla^2+k^2)\psi=0$$ is only separable in 11 coordinate systems. Similar statements can be found about the Laplace equation and maybe other ...
1
vote
1answer
17 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 ...
2
votes
1answer
35 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
0answers
23 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
45 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
22 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
60 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
53 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 ...
0
votes
1answer
22 views

Calculate the gradient of the curve

Calculate the gradient of the curve y=(x+1)^3 (x-1) at the points where it crosses the x-axis
19
votes
1answer
400 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
50 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
61 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
20 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
51 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 ...
-1
votes
1answer
18 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.