Welcome to Damian G's math analysis blog

Welcome to Damian G's math analysis blog

Tuesday, February 11, 2014

RWA Unit m concept 5: ellipses

Mathematical definition: The set of all points such that the sum of the distance from two points also known as the foci is a constant.

equation: (x-h)^2/a^2+(y-k)^2/b^2 for a "fat" ellipse (x-h)^2/ b^2+(y-k)^2/a^2
graphically: refer to above picture
description of key points: center-the center of the ellipse 2 vertices: the endpoints of the major axis Major Axis- the axis where the ellipse is wider crossing through the 2 vertices  Co vertices- points on an ellipse that lay on the minor axis   Minor Axis-axis on graph where ellipse is thinner co vertice to co vertice a is the bigger denominator and the major axis would be 2a units a B: B is the smaller denominator and the minor axis would be 2b units  away.
Foci: The father the foci are from each other the less ellipse will look like a circle and therefor the eccentricity of the ellipse will be closer to 1. ( the eccentricity of an ellipse should be between 1 and 0

One real world application of an ellipse is through an lithotripsy. Extracorporeal Shockwave Lithotripsy is a practice used by doctors in order to get rid of kidney and gall stones without the use of open surgery. This way the patient has less recovery time and less risk of infection. 

 The tool used for this is called a lithotripter. An ellipse is the base of this machine. Shockwaves are shot at one focus and are supposed to reflect to the other focus. A patients kideny or gallbladder should be placed at the other foci in order to recieve the shoackwaves The stone must be at precisly the focus in order for the machine to work. (http://mathcentral.uregina.ca/beyond/articles/Lithotripsy/lithotripsy1.html)