As of May 31, 2023, we have updated our Code of Conduct.

# Questions tagged [analytic-geometry]

Questions on the use of algebraic techniques for proving geometric facts. Analytic Geometry is a branch of algebra that is used to model geometric objects - points, (straight) lines, and circles being the most basic of these. It is concerned with defining and representing geometrical shapes in a numerical way.

6,330 questions
Filter by
Sorted by
Tagged with
11 views

### Parabolic Arc as a Product of 2 Latus Rectum Segments

I have been searching for any published work on this definition of a parabolic arc. The latus rectum of a parabola is a defining chord drawn parallel to the directrix and passes thru the focus. In the ...
1 vote
23 views

21 views

### Restricting maximum curvature of cubic bezier curve

Is there any way to reasonably restrict control points of cubic bezier curve so it's oscilating circle will never have radius smaller than r? Bezier curve with it's ...
71 views

48 views

### If diagonal points of a square are sliding on coordinate axes, locus of other two points

The full question is shown above. We have to try and write coordinates of A and C in terms of a single variable which we can later eliminate, but I'm unable to accomplish this. I tried using ...
32 views

### Find the point in $S=\{(x, y)| x, y \text{ are positive integers }\}$ which have the least possible distance sum from the points $(0,12)$ and $(8,0).$

Let $S=\{(x, y)| x, y \text{ are positive integers }\}$ viewed as a subset of the plane. For every point $P$ in $S,$ let $d_P$ denote the sum of the distances from $P$ to the point $(8,0)$ and the ...
70 views

48 views

### Why do the sign conventions in cartesian geometry work the way they do?

Usually in a Cartesian form of derivation in math and physics, I have seen that a particular formula is derived for simplicity by taking concerned points say in the first quadrant. Few examples are ...
1 vote
46 views

42 views

### Distance of centre of circle passing through points of contact of direct common tangents of two circles from the tangents.

We have this situation: where E is the center of the circle passing through the points of contact of the direct common tangents. A teacher claims that $x=\frac{r_1 +r_2}{2}$ and that it's true for ...
12 views

### How to find center of an arc given a geographical start point, end point and arc angle?

I am working in a way of drawing transitions in some kind of "Flight Plan" between two "waypoints" using the heading at the beginning of the arc and at the end of an arc. Given an ...
22 views

### Stereographic projection maps lines and circles on the plane into circles in the sphere

From pages $19$ and $20$ of Ahlfors' Complex Analysis: Why is the converse true? Why does any line or circle in the plane mapped into a circle in the sphere?
19 views

### How to find a set of linear inequalities from the vertices of a $d$-dimensional convex polytope?

Let $S = \{x_0, \dots, x_n\} \subseteq (\mathbb{R}^+)^{d}$ be the set of vertices of a convex $d$-dimensional convex polytope ($d \geq 2$). I am interested in finding a set of linear inequalities such ...
From page $19$ of Ahlfors' Complex Analysis: "[...] this equation takes the form [...] $$(\alpha_0-\alpha_3)(x^2+y^2)-2\alpha_1x-2\alpha_2y+\alpha_0+\alpha_3 = 0.$$ For $\alpha_0\ne \alpha_3$ ...