Fitting a conic to a given set of points using Trust Region method

A general conic can be uniquely describe by the following equation up to a scale factor: Ax^2+Bxy+Cy^2+Dx+Ey+F=0
Then (A,B,C,D,E,F) is often called algebraic parameter vector of the conic.

Usage: [ParA,RSS,iters,Jg] = TR_conic(XY,ParAini,DeltaIni)

Child functions:
Residuals_ellipse, Residuals_hyperbola, AtoG(can be found from previous submissions) , JmatrixLMA (included in the main function)

Input:
XY:given points<XY(i,1),XY(i,2)> i=1 to n
ParAini = [A,B,C,D,E,F]'- the initial parameter vector
DeltaIni: the initial size of the trust region.(this is optional; if it is missing, TR sets it to 1)

Output:
ParA: vector of algebraic parameters of the conic found
RSS: the Residual Sum of Squares (the sum of squares of the distances)
iters: the number of (main) iterations
Jg: the norm of the first derivative