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This question already has an answer here:

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

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marked as duplicate by user9660, MarcoB, m_goldberg, Öskå, Jens Jun 25 '16 at 16:53

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ It would help if you provide definition of f[x,y] and g[x,y]. Also your syntax seems to be incorrect. $\endgroup$ – e.doroskevic Jun 24 '16 at 10:08
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    $\begingroup$ Have you seen this? $\endgroup$ – J. M. will be back soon Jun 24 '16 at 10:08
  • $\begingroup$ 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. $\endgroup$ – Noghani Jun 24 '16 at 10:19
  • $\begingroup$ That's fine; you should still be able to use the functions in the linked thread on those. $\endgroup$ – J. M. will be back soon Jun 24 '16 at 10:26
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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

example

Reference

Curve Intersection

Show
Solve
ContourPlot
Graphics

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  • $\begingroup$ 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 $\endgroup$ – Noghani Jun 25 '16 at 7:02

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