# finding the coordinates of intersection point of two complicated implicit function [duplicate]

I have two complicated functions and i plot the contours of them like this:

ContourPlot[{f[x,y]==0,g[x,y]==0},{x,x1,x2},{y,y1,y2}]


I would like to find coordinates of intersection points exactly. I've tried most of solutions people suggested here before line Nsolve or FindRoot but it does not work and i am forced to get the coordinated by decreasing the domain and recognize the intersection point by eye !!! and use 'get coordinates' option !

I would appreciate if anybody helps me. Thanks

## marked as duplicate by user9660, MarcoB, m_goldberg, Öskå, JensJun 25 '16 at 16:53

• It would help if you provide definition of f[x,y] and g[x,y]. Also your syntax seems to be incorrect. – e.doroskevic Jun 24 '16 at 10:08
• Have you seen this? – J. M. will be back soon Jun 24 '16 at 10:08
• My functions are some pages if i want to put it here.But i can say that f and g are real and image part of a functions that contains multiples of bessel and hankel functions. – Noghani Jun 24 '16 at 10:19
• That's fine; you should still be able to use the functions in the linked thread on those. – J. M. will be back soon Jun 24 '16 at 10:26

## Example

Code

pts = Solve[y - 2 x^2 + 3/2 == 0 && {x, y} \[Element] Circle[{0, 0}, 1],{x,y}];
parabola = ContourPlot[{y - 2 x^2 + 3/2 == 0}, {x, -1.5, 1.5}, {y, -1.5, 1.5}];
intersections = {Red, PointSize[Medium], Point[{x, y} /. pts]};

Show[{parabola, Graphics[{Circle[{0, 0}, 1], intersections}]}]


Output

Reference

Curve Intersection

• Dear E.Doroskevic This solution is not suitable for mine.Because if you replace even a simple function like 3 y - 5 x^2 + 7/2 == 0 with Circle[{0, 0}, 1] it does not work. Anyway thank you so much – Noghani Jun 25 '16 at 7:02