Intersection of Two Implicit Curves over a domain

I have two implicit equations, one circle and one ellipse. I would like to know if there is a function or a way to find an intersection belonging to a given domain. Consider, for example:

circ = @(x,y) x^2+y^2-4 elp = @(x,y) ((x-2))^2+((y+2)/4)^2-1

There are two points of intersection (approximately):

P1 ~ (1.00 , -1.73) P2 ~ (1.46 , 1.37)

So I would like to know how to find P1, knowing it lies somewhere between: X: (0.8 , 1.2) Y: (-2 , -1)

OBS: I have no problems with numeric approximations, especially if it is not computationally intensive.

Thanks

Answer 1

[Teja Muppirala]

This sort of problem can be solved easily using FSOLVE

circ = @(x,y) x^2+y^2-4 
elp = @(x,y) ((x-2))^2+((y+2)/4)^2-1

fsolve(@(X)[circ(X(1),X(2)); elp(X(1),X(2))],[1 -1.5])

This returns

ans =
  1.0023   -1.7307

[Ankit Singh]

Can we use this without having to enter the probable range, i.e. [1 -1.5]? Also can this method be used for 2 ellipses?

[Sudhanshu Verma]

But there are 2 point of intersection, how would you find the second one

Answer 2

[Rodrigo]

that was just what i needed! thanks!

[Fenil Patel]

can this method used for two intersecting cylinder??