Register to reply

Ellipse through three points

by Nelourir
Tags: ellipse, points
Share this thread:
Jul5-11, 07:04 AM
P: 6
1. The problem statement, all variables and given/known data

First of all, I'm not sure the following is achievable at my level (last year of high school), as it is not posed as a direct question, but if yes, could you point me in the right direction?

I'm trying to find an ellipse that goes through three points, (0,0) , (b,0) and (b/2,h).
This actually represents a building with a base of width b and a height of h.

The building is symmetrical, therefore the ellipse is not 'rotated' (I'm not sure how to express this mathematically).

3. The attempt at a solution
Using the equation for an ellipse (not trying to confuse anyone but h is not H and b is not B):
(((X-H)^2)/(A^2)) + (((Y-K)^2)/(B^2)),
I find the following (using logic and no algebra):

H is b/2 as the centre of the ellipse always goes through the line x=b/2
A is greater than or equal to b/2. (otherwise the ellipse cannot touch both points on the x axis)
B is greater than or equal to h. (I don't want the building to have angles greater than 90o)
Using the above statement, I expressed B as h + C and found that K = -C.

I realise there is an infinite number of ellipses (at least I'm assuming so), but I think that A should be dependent on b, h and/or C. Could you help me find this?

Thank you for your help.

EDIT: OK, I think I found my answer by replacing A by b/2 + D, plugged in x=0, y=0 then I rearranged until it looked like a quadratic equation with D as the 'variable' and I got an answer for D in terms of b, h and D. Sorry for making a new topic .
Phys.Org News Partner Science news on
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100

Register to reply

Related Discussions
Calculate ellipse from 4 points? Differential Geometry 4
Build an ellipse given 3 points and the focus General Math 8
Ellipse given n minimum points and knowing one of the focus General Math 0
3d ellipse given two points Differential Geometry 1
Points on an ellipse Calculus & Beyond Homework 4