Questions on the use of algebraic techniques to prove geometric theorems.
0
votes
2answers
444 views
Urgent - Find the equation of the lines tangent to a circle
Question: 'Find the equation of the lines from point $P(0,6)$ tangent to the circle $x^2+y^2=4x+4$.
So what I did firstly is rewrite it to the form $(x-2)^2 + y^2 = 8$, and I saw that point $P$ is ...
1
vote
0answers
45 views
Solving inverse square of visible scale
I'm not super-adept in mathematics, so I turn to you for help. As I read, the perceived scale of an object reduces by the inverse square as the viewed distance increases. In order to solve for this, ...
2
votes
0answers
65 views
Algebraic Geometry studied via Filters
Is there any research relating varieties with filters instead of radical ideals? For example, Suppose we have a variety V in C^n, now consider the fixed filter consisting of all algebraic sets ...
0
votes
2answers
164 views
Can you suggest me a good book for self-study of analytic geometry 1?
I'm stuyding mathematics alone, but I plan to enter in the university in the near future, I went to the university website and it suggests Analytic Geometry 1 as part of their curricula, the topics ...
2
votes
2answers
127 views
How to define a perspective circle in xy?
You can see a perspective view of a square(FCED) and a circle in 2D screen. O is center of the circle.
How can I define the perspective circle equation that shown as red in the picture?
Thanks a ...
1
vote
2answers
155 views
The intersection of a line with a circle
Get the intersections of the line $y=x+2$ with the circle $x^2+y^2=10$
What I did:
$y^2=10-x^2$
$y=\sqrt{10-x^2}$ or $y=-\sqrt{10-x^2}$
$ x+ 2 = y=\sqrt{10-x^2}$
If you continue, $x=-3$ or ...
1
vote
1answer
746 views
Analytic Geometry: Circle
Given is a line with parametric equation:
$ x = 2 \lambda $
$ y = 1-\lambda $
Find out for which values of $\lambda$ the line is inside the circle of $x^2+4x+y^2-6x+5=0$
My attempt at solving ...
2
votes
4answers
410 views
Get the equation of a circle when given 3 points
Get the equation of a circle through the points $(1,1), (2,4), (5,3) $.
I can solve this by simply drawing it, but is there a way of solving it (easily) without having to draw?
0
votes
4answers
249 views
Analytic Geometry: Distance between a point and a line.
Get the equations of both lines going through $0$ which have a distance of 5 from the point $(1,7)$.
How to handle this problem? We have this formula:
If line $l$ is $ax+by=c$, distance $ P(x,y) $ ...
1
vote
3answers
2k views
Common tangent to two circles
Find the equations of the common tangents to the 2 circles:
$$(x - 2)^2 + y^2 = 9$$
and
$$(x - 5)^2 + (y - 4)^2 = 4.$$
I've tried to set the equation to be $y = ax+b$, substitute this ...
0
votes
2answers
68 views
Problem involving points on a line.
Given two points A(-3,4) and B(2,5) find the coordinates of one point P on the line and passing por A and B. Look that the point P is two times more distant from A than B.
1
vote
1answer
89 views
Finding two points that have a defined distance between two intersecting lines
I was given a test yesterday, a test which unfortunately I was unable to study to. In it was a question that was too hard that it became our homework for the whole week.
It says that on lines ...
3
votes
1answer
87 views
Offsetting a curve in 2D
I'd like to "move" a curve $d$ (offset) units "up" (actually in the sense that the perpendicular distance between the curves is always constant). The objective is to create a channel that has constant ...
1
vote
3answers
116 views
Number of ellipses through two fixed points in 2D space?
How many ellipses with a given size (mean $a$ and $b$ given) one can draw through two fixed points in 2D plane?
0
votes
0answers
49 views
Please help with this vector question
The points A, B and C have position vectors a=(2,1,2) b=(-3,2,5) and c=(4,5,-2) respectively, with respect to a fixed origin. The point D is such that ABCD, in >that order, is a parallelogram.
...
0
votes
3answers
778 views
Find if the points are collinear
Find if the points joining $A=(6,7,1), B=(2,-3,1)$ and $C=(4,-5,0)$ are collinear.
how to prove that? Anyone, please help me!
0
votes
3answers
539 views
Show by using vectors that the two diagonals of a square are equal in dimension
and also perpendicular to each other?
how can we prove that ...please Help me
2
votes
2answers
201 views
Pattern matching circle, square or triangle
I have a set of x, y co-ordinates that are actually taken from hand drawings of a circle, square or a triangle. Using the set of points, I need to mathematically find if the points approximately fit a ...
0
votes
2answers
57 views
What are the coordinates of vertex C
Triangle $ABC$ has 2 given vertices, $A(1,1)$ and $B(5,3)$. Also, AC=BC and $\angle ACB = \,^{\circ}\mathrm{90}$.
The triangle is in the first quadrant entirely. What are the coordinates of vertex ...
2
votes
2answers
137 views
Analytic Geometry question I can't solve
An isosceles triangle $ABC$ has 2 given vertices, $A(3,2)$ and $C (7,14$). The slope of AB is $\dfrac{1}{2}$. What are the coordinates of B?
I could figure out that line AB = $\dfrac{1}{2}x + ...
0
votes
1answer
88 views
Find the coordinates of P
There is a point P on the line $5x-3y=7$ that is equally far from the points $A(1,4) $ and $ B(3,10)$.
Find the coordinates of P.
What I did:
$5x-3y=7$ is the same as $ y = ...
0
votes
6answers
38 views
Finding the slope of a function
How do I find the slope of this function:
$px + (2p-1)y + 4 = 0$
I need to know how to answer a previous question of mine (also posted on this forum)
0
votes
5answers
48 views
Determine a parameter in such a way that two lines are parallel
The lines
$px + (2p-1)y + 4 = 0$
and
$(p+3)x + 2py + 6 = 0$
are parallel to each other. Find $p$.
I have no idea how to tackle this problem, can anyone help?
1
vote
1answer
34 views
How to figure out x and y components of a vector
Given a vector $\vec{v}$ and an angle $\alpha$ between the vector and $Oy$ or $Ox$ what is the quickest way to figure out the projections, or the $x$ and $y$ components?
4
votes
2answers
138 views
Locus of points generates several very different curves. Closed form?
Consider, for the sake of simplicity, a circle $C$ centered at he origin with radius $a$. Let $F=(h,k)$ be a point not necessarily inside the circle. Let $M=(a\cos\theta,a\sin\theta)$ be a point in ...
1
vote
1answer
68 views
Locus perpendicular to a plane in $\mathcal{R}^4$
I have solved an exercise but I'm not sure to have solved it perfectly. Could you check it? It's very important for me..
In $\mathcal{R}^4$ I have a plane $\pi$ and a point P. I have to find the ...
1
vote
0answers
41 views
figuring out the sum of angles from the addition of geometrical shapes within a circle
if you add a number with another you get the sum of the two.(1+1=2, 2+2=4) right?
but if you take a circle and put a horizontal line through it you have 4 angles in it. put another circle with a ...
2
votes
4answers
1k views
How to know if a point is inside a circle?
Having a circle with the centre $(x_c, y_c)$ with the radius $r$ how to know whether a point $(x_p, y_p)$ is inside the circle?
2
votes
1answer
80 views
Hard calculating about bisectors
I need to find intersection point of two bisectors of KL, KC and CL line.
Coordinates : $C(2a+2, 2b), L(2-2a, 2b)$ and $K \left( \frac{2(a^3 - a^2 + ab^2 + b^2)}{a^2 + b^2}, 2 - \frac{4a}{a^2 + ...
0
votes
1answer
306 views
intersection point between circle and line
The line $-bx + ay + 2b = 0$ intersects circle on points A and B. Circle equation is $$(x-1)^2 + \big(y-\frac{a^2 + b^2 - a}{b}\big)^2 = \frac{(a^2 + b^2 - a)^2 + b^2}{b}$$
or after ...
2
votes
3answers
88 views
Simple analytic geometry question I need help with
Give the equation of a circle with the center $ (a,0) $ which is tangent to the line $ y = x $
I now have $ (x-a)^2 + y^2 = r^2 $ but I don't know how to continue.. please help!
2
votes
2answers
35 views
Trouble with formulation of an analytic geometry question
I'm having trouble understanding a certain question, so I am asking for an explanation of it. The question is asked in a different language, so my translation will probably be mistake-ridden, I hope ...
0
votes
3answers
68 views
Mathematical 'language' (geometry)
What does this question mean:
'Show (translated from my native language) that the equation $ x^2 - 4x + y^2 + 6y = 51 $ is a circle.' I have absolutely no idea how to 'show/prove/etc.' it, other than ...
1
vote
3answers
71 views
How to get the equation of a circle with the given information
You have a center of a circle $M(-2,3)$ going through a point $P(1,7)$.
What is the equation of the circle?
I thought you could solve it by $R^2 = 3^2 + 4^2$, but that would just give a radius of 5 ...
1
vote
2answers
43 views
An analytic geometry question + algebra
We have a Cartesian coordinate system with the points M (a,b) Q (4,2) and P (x,y) but I don't think you need P to solve this one, only M and Q. M is the middle of a circle with a radius r, and Q is a ...
0
votes
0answers
88 views
Analytic Geometry Question
There is a point $M (2,1$) on a Cartesian coordinate system. There is also a point $P (x,y)$. What is the distance $MP$ in $x$ and $y$?
I can figure out that $ PM^2$ = $(x-2)^2 + (y-1)^2$, at least, ...
0
votes
3answers
126 views
How to find on which outer side of the rectangle falls the point?
Qt has a class QRect which tells whether the point is inside the rectangle or not.
Now, the problem is to find out on which ...
0
votes
0answers
55 views
Eccentricity and Length of Semi Axes of a conic
If a conic $ax^2+by^2+2hxy+2gx+2fy+c=0$ and say:
How to find the eccentricity and the semi-axes of this conic. I do understand that if its a hyperbola only one of the semi axes will be real.
Soham
6
votes
7answers
293 views
Detect when a point belongs to a bounding box with distances
I have a box with known bounding coordinates (latitudes and longitudes): latN, latS, lonW, lonE.
I have a mystery point P with ...
3
votes
0answers
65 views
packing for the polytope
Let $X=(X, \|\cdot\|)$ be some normed space. Let $C=[-1,1]^n$ and $H$ be a plane with equation $\sum_{i=1}^nr_i=s, 1\le s\le n.$ (Here $r_i$ are such that $Proba(r_i=1)=Proba(r_i=-1)=1/2$). The ...
5
votes
3answers
423 views
A simple(?) Analytical Geometry Question (Ellipse) my teacher can't solve
Here's the story:
I am a high school student who absolutely loves math. So I took a university level mathematics course that is renowned throughout our school for being extremely rigorous and tough. ...
0
votes
1answer
107 views
Finding coordinates of some points in picture
Let $A(0,0)$, $B(2,0)$, $C(c_{x}, x_{y})$, $D(d_{x}, d_{y})$.
$O_1$ and $N$ is the center of circles (ABD) and (CKL).
Find coordinates of $C, N, K, L, O_1$.
3
votes
0answers
105 views
Illustrations of a line and a curve intersecting for complex field
Are there nice illustrations on the Net of say $y=a·x+b$ and $y=x^2$ intersecting where x and y are complex? I'm thinking of the amplitude of y being depicted as height above the complex plane with ...
0
votes
1answer
95 views
locate a audio source by 3 microphones, same plane, by using the volume
Let have 3 microphones
MIC1: @ mic1x,mic1y
MIC2: @ mic2x,mic2y
MIC3: @ mic3x,mic3y.
MIC1-MIC2 separated 2500mm at 90degr
MIC2-MIC3 separated 2500mm at 90degr
If a sound produced by source S reach ...
60
votes
18answers
5k views
How to check if a point is inside a rectangle?
There is a point (x,y), and a rectangle a(x1,y1),b(x2,y2),c(x3,y3),d(x4,y4), how can one check if the point inside the ...
4
votes
3answers
666 views
Find a plane perpendicular to a plane passing by point
In $\mathbb R^4$ I have: $$\pi: \begin{cases} x+y-z+q+1=0 \\ 2x+3y+z-3q=0\end{cases}$$
I have to find $\pi' \bot$ $ \pi $ and passing by $P=(0,1,0,1)$. How can I do that? Thanks a lot!
2
votes
1answer
93 views
Showing: point of polytope which maximizes the minimum distance to a vertex is a barycentre?
Let $T_1$ and $T_2$ be two regular $(n-1)$-dimensional simplices with vertices $$(t,0,\ldots,0), (0,t,\ldots, 0),\ldots, (0, 0, \ldots, t),$$ and $$(t-n+1,1,\ldots, 1), (1, t-n+1, \ldots, 1), \ldots, ...
1
vote
1answer
110 views
How to find intersection of an ellipse and a line that passes through the foci
There are two lines, parallel to the $x$-axis, which pass through the foci and intersect the ellipse at four points. How can I find the points of intersection?
vertex: $(0,0)$
foci: $(0,10)$ and ...
