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I made some small bug fixes to the conic intersection package. Thanks to Dany for pointing the bug out. The matlab code that you can download here can be used to detect the (up to) four intersections of two conics. The usage is quite straightforward but anyway, here is an example:

%%the homogeneous representation of a conic is a matrix
%% m = [A C D; C B E; D E F] that represents the equation
%% A x^2 + B y^2 + 2C xy + 2D x + 2Ey + F = 0

%a circle centered in the origin
E1 = [1 0 0; 0 1 0; 0 0 -3]

%an ellipse centered in the origin
E2 = [1 0 0; 0 3 0; 0 0 -6]

%get the four homogeneous intersections
P = intersectConics(E1, E2)
%plot the normalized points
plot(P(1,:) ./ P(3,:) , P(2,:) ./ P(3,:), 'ro');

• Conics intersections v.1.02