3
votes
2answers
31 views

Midpoint of chord of contact

Question: The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4x - 5y = 20$ to the circle $x^2 + y^2 = 9$ is: a) $20(x^2 - y^2)- 36x + 45y = ...
0
votes
1answer
52 views

Enlarge 3 Circles about the same factor to find the Intersect

I currently have 3 circles that not intersect at all. Like this: Now i would like enlarge the circles about the same factor to find the intersection of this three circles. I have tried following ...
0
votes
0answers
23 views

Position vectors of sphere/circle touching central one

I am trying to understand the meaning of an expression describing the "kissing" number problem. On Wiki, it states the following: Let $x_n$ be a set of $N$ $D$-dimensional position vectors of the ...
1
vote
2answers
35 views

Determining points on a circle in a particular plane

This is more of a computer graphics question really, but I was just wondering the efficient way to determine n equally spaced points on a circle, given a normal vector to the circle and the radius of ...
1
vote
2answers
76 views

Calculate center of circle tangent to two lines in space

Good afternoon everyone! I am facing a problem which is straining my memory of linear algebra. I have: Three points with known coordinates, forming a triangle in space. Let the coordinates be ...
0
votes
1answer
40 views

Finding equations when given new center of a circle

$y = −x + \sqrt{2}$, $y = −x − \sqrt{2}$, $y = x + \sqrt{2}$, and $y = x − \sqrt{2}$. These equations determine lines, which in turn bound a diamond shaped region in the plane. Construct a diamond ...
0
votes
0answers
48 views

Finding three collinear points passes through three circles

Assume that we have three collinear points $A(x_0,y_0),B(x_1,y_1)$ and $C(x_2,y_2)$. They are on three different circles whose centres and radii are respectively $\big((P_x, P_y), r_P\big)$, ...
1
vote
1answer
18 views

Make a point orbit another point, given time and a normal.

I am working in 3D space. I am trying to make a solar system model. known variables: center of orbit, C (x,y,z) normal, perpendicular to the orbit, N (x,y,z) radius of orbit, R time, position ...
2
votes
1answer
137 views

Equation for concentric circles?

I want an equation for concentric circles. In following image I am trying to draw concentric circles in Java but as you can see these are messed up. This is because their (x,y) coordinates (i.e. ...
1
vote
1answer
157 views

Finding equation of the image under a linear transformation

The equation of C is $x^2 + y^2 =1 $ How do I find the equation of the curve $C'=f(C)$ This is the image of $C$ under the linear transformation $f$ represented by the matrix $A=\begin{bmatrix}2 & ...
0
votes
2answers
48 views

Question on inscribed equilateral triangle

Question: $ABC$ and $ODE$ are equilateral triangle with $BC || DE$. If $O$ is the center of the circle, then find the ratio $AQ:QC$ So, my thought on this is that, since we are not given the ...
2
votes
3answers
172 views

Find radius of a circle which is tangent to three known lines

I need to find the equation for a circle which is tangent to the following three lines: y=0 x=0 y=-x+0.338334 For the last tangent line equation, I know that it is tangent at the point (0.169167, ...
0
votes
4answers
63 views

Trouble in this circle question

Referring to this diagram (self-made): Question says: In the given figure diameter of the circle is $3$ cm. AB & MN are two diameter such that MN is perpendicular to AB. In addition CG is ...
0
votes
1answer
83 views

Great circle and how to “imagine” it in this case?

I am currently working on a riddle. I have to search and locate a person, but I do not know, where he is. I only have some informations, concerning the probability where he might be. A satellite ...
1
vote
2answers
168 views

Why the unit circle in $\mathbf{R^2}$ has one dimension?

When I was reading 'Convex Optimization, Stephen Boyd', I was wondering of following steps Consider the unit circle in $\mathbf{R^2}$, $i.e.$, $\{x\in\mathbf{R^2}|x^2_1+x^2_2=1\}$. Its affine hull ...
2
votes
1answer
102 views

Find the point of a circumference following the line from center to a point in the circle

The purple circle dignifies a known center point. If I choose a point at random inside the circle, is it possible find the orange square (The point where the green line intersects with the ...
1
vote
2answers
341 views

Calculating circle in taxicab geometry

I struggle with the problem of calculating radius and center of a circle when being in taxicab geometry. I need the case for two and three points including degenerate cases (collinear in the three ...
1
vote
1answer
52 views

Unit circle - how to prevent backward rotation

Let's assume we have a unit circle (0, 2$\pi$). Basically I have a point on this circle who is supposed to move only forward. This point is controlled by the user mouse and constantly calculate 25 ...
0
votes
1answer
63 views

How to find the n number of coordinates of circumference of circle?

Line AB has two coordinates A = (1,3) and B = (1,6). How to find 10 uniform coordinates of a circumference of circle whoose radius is AB. Edit I tried this link but didn't get it.
2
votes
0answers
42 views

Bijection from the plane to itself that takes a circle to a circle must take a straight line to a straight line

Prove, that a bijection from the plane to itself that takes a circle to a circle must take a straight line to a straight line. There exists an elementary proof? I know this question can be found here ...
0
votes
1answer
71 views

what are the various fields in which circle is treated as infinite sided regular polygon?

What are the various fields in which circle is treated as infinite sided regular polygon? What I actually mean is , "can u suggest me some applications where circle is treated as infinite sided ...
1
vote
2answers
77 views

How can I calculate the points of two lines that connect two circles?

Let's say I have two circles of equal or differing radii, a variable distance apart. I want to calculate the end points of two lines, that will "connect" the circles. And no matter how the ...
3
votes
1answer
82 views

Check If a point on a circle is left or right of a point

What is the best way to determine if a point on a circle is to the left or to the right of another point on that same circle?
0
votes
1answer
774 views

Find the equation of a circle given the radius and center (with vector length notation)

I want to find the equation but use vector length notation and I'm not sure about how to write it. $$ a) r = 2, A(-1; 1)$$ the line I'm not sure - $$|[x-x_0 , y-y_0]|^2 = r^2$$ then I do $$(x+1)^2 + ...
0
votes
1answer
92 views

Minimal rotation to avoid collision of circles

The discriminant of a certain quadratic equation which determines when two circles (hyperspheres?) will collide, provided they travel with a constant velocity is $$(\Delta v\cdot\Delta s)^2-(\Delta ...
1
vote
1answer
350 views

Meaning of this 4x4 determinant

Let $p,q,r$ and $s$ be four points on the plane. Moreover, $p,q,r$ are given in clockwise order. My book said that the following determinant is positive if and only if $s$ lies inside the circle ...