Ellipse and circle intersection
- To: mathgroup at smc.vnet.net
- Subject: [mg38358] Ellipse and circle intersection
- From: Tomas Garza <tgarza01 at prodigy.net.mx>
- Date: Thu, 12 Dec 2002 01:38:07 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
A correspondent has sent me the following problem.
"I want to calculate the intersection of an ellipse ((x-c)^2/b^2 +
(y-d)^2/a^2 ==1) with centre at the point (c,d) and a circle (x^2 +
y^2 == 1) with centre at(0,0). What are the formal point
solutions?".
I thought the problem was straightforward and wrote
ellipse = (x - c)^2/b^2 + (y - d)^2/a^2 == 1;
circ = x^2 + y^2 == 1;
sol = Solve[{ellipse, circ}, {x, y}];
The output comes out immediately as a rather long expression. However,
when trying to obtain numerical values for given values of a, b, c, and
d, I get complex numbers, and even in the case where their imaginary
part is close to 0, the real part doesn't correspond at all to the
solution (as seen in an implicit plot of the two figures). I'm at a
loss!
What's going on?
Tomas Garza
Mexico City