Tagged Questions
7
votes
4answers
116 views
closest point to on $y=1/x$ to a given point
I feel like I'm missing something basic - given a point $(a,b)$ how do I find the closest point to it on the curve $y=1/x$? I tried the direct approach of pluggin in $y=1/x$ into the distance formula ...
1
vote
1answer
176 views
find the center of an ellipse given tangent point and angle
I have an ellipse with known major radius $r_y$ and minor radius $r_y$, aligned with the x- and y-axis.
Given a tangent point $T$ and the tangent angle $\alpha$, how do I calculate the center $C$ ...
5
votes
0answers
63 views
What property does this equation calculate?
It's pretty difficult to Google for the meaning of a formula.
This is the equation, it has to do with ellipses and GIS coordinates.
$$\nu =\frac{ a} {\sqrt{(1 - (e^2 \cdot \sin(\varphi))^2)}}$$
$a$ ...
3
votes
0answers
140 views
Ellipse and circles
Playing with an ellipse I discovered the following properties and am now looking for a nice proof or references.
Let's consider an ellipse with foci $A$ and $B$ and let $C$ be a point on it. Let $l$ ...
17
votes
2answers
908 views
Intersection of two parabolae
Problem:
Consider two parabolae such that their axes of symmetry form a right angle. Prove that all four points of intersection lie on a common circle (it is an assumption that there exist such four ...
3
votes
3answers
4k views
Check if a point is within an ellipse
I have an ellipse centered at $(h,k)$, with semi-major axis $r_x$, semi-minor axis $r_y$, both aligned with the Cartesian plane.
How do I determine if a point $(x,y)$ is within the area bounded by ...
2
votes
1answer
361 views
Property of an ellipse
I need proof for the following question. Also, I want to know, can we apply the same for other conics. If yes, where and when... Please explain.
Show that there exists a point K on the major axis of ...
8
votes
3answers
734 views
Minimal Ellipse Circumscribing A Right Triangle
Find the equation of the ellipse circumscribing a right triangle whose lengths of it's sides are $3,4,5$ and such that its area is the minimum possible one.
You may chose the origin and orientation ...
