0
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0answers
28 views

Co-Ordinate Geometry Doubts

Facing trouble to find a solution for my problem. I am asking here. I hope I will get at least a clue for my question. I have two points $(x_1,y_1),(x_2,y_2)$ and the distance between them is $r$. The ...
-2
votes
1answer
34 views

The locus of points with given sum of squares of distances to two fixed points

$A(a,b)$ and $B(b,-a)$ are two fixed points. If $P(x,y)$ is a moving point such that $$|AP|^2 + |PB|^2 = |AB|^2 \tag1$$ prove that $x^2 + y^2 =(b-a)(x+y)$. So far I tried to use distance formula ...
1
vote
1answer
31 views

How to find the angle between two vectors?

Here, I would like to describe my requirements .. Let's say we have two vectors named $\bf A$ and $\bf B$. Two vectors are in different magnitude and opposite directions and lay on different planes. ...
1
vote
1answer
25 views

What is the basic idea of homogenisation of an equation?

I do get that when you are homogenising it makes it in an equation of pair of straight lines passing through origin but what is its actual point and its applications?
0
votes
1answer
34 views

Coordinate Geometry of circles; Radical Axis question

If one of the diameters of the circle $x^2+y^2-2x-6y+6=0$ is a chord to the circle with center at $(2, 1)$, then the radius of the second circle is? Apparently the solution is $3$, with the ...
0
votes
1answer
20 views

Coordinates rotation and function change

In the Cartesian coordinates $(x,y)$, I have a vector function $\bar{f}(x)=\hat{x}A\cos(yk)$, where $A$ and $k$ are constants. I make now a 45 degrees rotation (in the same plane) to the new set of ...
1
vote
1answer
38 views

Equation of pair of reflected straight lines given the equation of pair of incident straight lines

If $ax^2 + 2bxy + by^2 = 0$ represents a pair of lines, then find the combined equation of lines that can be obtained by reflecting these lines about the x-axis. I know that this can be done by ...
0
votes
1answer
45 views

Geometric interpretation of a complex solution

A straight line in 2-D $x+y=3$ and a circle in 2-D $x^2+y^2=4$ do not have a point of intersection in the plane containing the two. But on solving these equations analytically, on gets 2 complex ...
-2
votes
1answer
29 views

Distance to the point of intersection of two altitudes in a triangle

Problem $P,Q,R$ are the points $(4,2)$, $(2,1)$ and $(6,-3)$. Also, $PS$ and $QT$ are altitudes in this triangle. A) Find the equations of PS and QT My answer: PS: $y-x-2=0$, QT: $5y-2x-1=0$ ...
1
vote
1answer
29 views

A rectangle $OACB$ with two axes as two sides,the origin $O$ as a vertex is drawn in which the length $OA$ is four times the width $OB$…

A rectangle $OACB$ with two axes as two sides,the origin $O$ as a vertex is drawn in which the length $OA$ is four times the width $OB$.A circle is drawn passing through the points BC and touching ...
0
votes
3answers
24 views

A question on co-ordinates of intersecting lines…Given in picture below

Please do also MENTION how you got the solution.........
0
votes
1answer
21 views

Points defined by relations (an exercise from “System of Coordinates”)?

An exercise from "System of Coordinates" (by Gelfand, Glagoleva and Kirilov) asks me to "[t]ry to decide by yourself which sets of points are defined by these relations" and relations given are: a. ...
5
votes
1answer
134 views

Coordinate Transformations

I am physics student. My mathematical background is quite weak. I just want to know the similarities (if there are any) between coordinate transformation of two kinds : Rotation of coordinate (and ...
0
votes
1answer
43 views

Fixed points through a general circle.

The circle $C: x^2 + y^2 + kx + (1+k)y - (k+1)=0$ passes through two fixed points for every real number $k$. Find $(i)$ co-ordinates of these two points and $(ii)$ the minimum value of the radius.
1
vote
2answers
114 views

Using the Invariant Principle to prove a coordinate can't be reached

The problem is as follows: A robot wanders around a 2-dimensional grid. Starting at (0, 0) he is allowed 4 different kinds of step: 1. (+2, -1) 2. (+1, -2) 3. (+1, +1) 4. (-3, 0) He is trying to get ...
0
votes
1answer
46 views

Given the coordinates of two of three collinear points such that $PM=MQ$, find the third point

P,M and Q are three collinear points and PM=MQ. If P is the point (-1,4) and M is the point (5,8), find the coordinates of the point Q. What I've Done: I've found the distance MQ which is ...
1
vote
1answer
70 views

show that the straight lines $(a^2-3b^2)x^2+8abxy+(b^2-3a^2)y^2=0$ form with the lie $ax+by+c=o$ an equilateral triangle

show that the straight lines $(a^2-3b^2)x^2+8abxy+(b^2-3a^2)y^2=0$ form with the lie ax+by+c=o an equilateral triangle whose area is $\frac{c^2}{\sqrt{3}(a^2+b^2)}$ is there any other way to solve ...
0
votes
2answers
159 views

equation representing 2 straight lines

Let us assume this equation is given to us we have to factorize it $$12x^2 +7xy-10y^2+13x+45y-3=0$$ By solving we get that this represents two straight lines. But how to factorize it? Is there a ...
0
votes
1answer
243 views

How to show that a line pass through a point?

How to show that a line pass through a point? Two fixed straight line $OX$ and $OY$ are cut by a variable line at the points $A$ and $B$ respectively and $P$ and $Q$ are the feet of the ...
0
votes
0answers
13 views

The velocity of a set of axes with respect to themselves

I am reading Whittaker's Analytical Dynamics. This is chapter 8 Non Holonomic Systems. Dissipative systems. Paragraph 88 is Equations of motion relative to axes moving in an arbitrary way. Let $G$ be ...
2
votes
1answer
125 views

Find the locus of the point which divides segment AB internally in the ratio 1:2.

A and B are variable points on X and Y axis respectively,such that l(ab)=4.Find the locus of the point which divides segment AB internally in the ratio 1:2. I think that it must be a circle . or ...
3
votes
1answer
127 views

Are cartesian coordinates “more fundamental” than other coordinates, and are they inherently tied to $\mathbb R^n$?

Are the Cartesian coordinates more "fundamental" than other coordinate systems? When someone says $\mathbb R^n$ do we implicitly mean the set of points PLUS Cartesian coordinate system? Sometimes I ...
0
votes
1answer
67 views

Measuring distances on any coordinate system

I was reading the book The ABC of Relativity from Betrand Russell, and at some point, the author mentions a method for measuring the distance between 2 points on any coordinate system. He says that ...
0
votes
2answers
544 views

Linear equations; how to write an equation from given coordinates?

A straight line goes through the points $( 0, 1 )$, $( 2, 7 )$ and $( 4, 13 )$ and I need to write the equation of this straight line. How do you write equations? I know you have it's usually $y = x ...
1
vote
2answers
912 views

Finding the locus of the midpoint of chord that subtends a right angle at $(\alpha,\beta)$

There is a circle $x^2+y^2=a^2$. On any line that cuts the circle in two distinct points(it is a secant), the points of intersection with circle are taken and at those two points I draw the tangents ...
0
votes
1answer
245 views

Find a locus of points to satisfy these conditions?

So, we have to straight lines: $$3x-4y+5=0$$ $$2x+3y-4=0$$ You have to find a locus of points from which all perpendiculars to the two lines given are in a 2:3 ratio.
1
vote
1answer
234 views

Intersection of two lines

What is the suggested method to find the intersection of two line *segments in 3D space programmatically? I mean there are various methods to solve a set of 2 linear equations, eg. Using ...
0
votes
2answers
134 views

How to check if a line is coinciding with another line?

I asked a question on stackoverflow about how to know if a line is coinciding with another polygon. [http://stackoverflow.com/q/13304575/1362544] The answer I got suggested checking intersection of ...
1
vote
0answers
117 views

Circle-Circle intersection coordinate system

Consider two points in the 2D Euclidean plane, the origin $0$ and $x$. One can define a co-ordinate system such that for any point $y$ in the plane, $y$ is parametrized by its distance from $0$, call ...
0
votes
2answers
222 views

Help me with Cylinder -coordinates problem, back to Cartesian or not? How to do it fast?

Source of the problem, 3b here. Problem Question Electricity density in cylinder coordinates is $\bar{J}=e^{-r^2}\bar{e}_z$. Current creates magnetic field of the form ...
1
vote
0answers
1k views

Direction ratio of a vector in 3d?

Suppose I have a vector whose starting end is the origin & the other end can be in any of the 8 quadrants (in 3d). I can easily get direction ratios for the vector & also know in which ...
0
votes
2answers
186 views

Vector Geometry - relation between a point and a line with angle and one known point on it

I have two problems I will be very grateful if somebody helps me about them. If I have a line $L_1$ with a known point $(x_1, y_1)$ on it and has slope $\theta_1$, how do I know if a point $P=(x, y)$ ...
2
votes
2answers
4k views

How do we prove the rotation matrix in two dimensions not by casework?

I was trying to prove: To carry out a rotation using matrices the point $(x, y)$ to be rotated from the angle, $θ$, where $(x′, y′)$ are the co-ordinates of the point after rotation, and the formulae ...