I did make a mistake. The matrix of the second conic was wrong so your code cannot find the intersections. I checked my code and I found that the matrix of the second conic should be
E2 =[ -0.1642 0 0.1642;
0 8.8358 -15.4627;
0.1642 -15.4627 26.3578]

After receiving your email, I checked my code and corrected the second matrix. YOUR CODE WORKED PERFECTLY AND GAVE THE EXACT SOLUTION. Here is the result.

http://imageshack.us/a/img401/8209/83223264.png

Thank you very much for sharing your code and I really appreciate your kindness to reply my email and help me solve the problem.

This function is not vectorized, does not check arguments, has no help, and does not employ the most robust algorithm. This topic has been discussed at length on CSSM. e.g., here:
http://www.mathworks.com/matlabcentral/newsreader/view_thread/151925#805660

Comment only