Intersection Ellipse & Circle

*To*: mathgroup at smc.vnet.net*Subject*: [mg32503] Intersection Ellipse & Circle*From*: Philipp Schramek <philipp at physics.usyd.edu.au>*Date*: Thu, 24 Jan 2002 05:20:56 -0500 (EST)*Organization*: The University of Sydney, Australia*Sender*: owner-wri-mathgroup at wolfram.com

Hi I want to calculate the intersection of an Ellips ((x-c)^2/b^2 + (y-d)^2/a^2 ==1)which centre is at the point (c,d) and a Circle (x^2 + y^2 == 1) which centre is (0,0). I thought I might be able to solve this problem for any a!=0 && b!=0 with Mathmatica 3. There should be 4 solutions. Therefore I did following calcuatlion: In[15]:= Eliminate[{y==Sqrt[1-x^2],((x-c)^2)/(b^2) + ((y-d)^2)/(a^2) ==1},y] 2 Out[15]= a != 0 && b != 0 && c - 2 c x == 2 2 2 2 2 2 2 2 b b d 2 b x 2 b d Sqrt[1 - x ] > b - -- - ----- - x + ----- + ------------------- 2 2 2 2 a a a a In[16]:= Solve[%,x] Out[16]:= ..................... My problem is that the solutions I got from Mathmatica are very very long and therefore far to long for me to use it as a analytical approach. In fact I was very suprised that there was not an easier solution. Even if I assume the special case b==1 the results were too long.I even tried to solve the problem defining the circle and the ellips by two angles: Eliminate[{Cos[x]==a*Cos[y]+c, Sin[x]==b*Sin[y]+d},y] But solving this result was even worse. Does anyone has a suggestion how I could get a shorter result for my problem? Thanks for you help Philipp

**Follow-Ups**:**Re: Intersection Ellipse & Circle***From:*Tomas Garza <tgarza01@prodigy.net.mx>

**Re: Intersection Ellipse & Circle***From:*Daniel Lichtblau <danl@wolfram.com>