# Using IntervalArithmetic to find the number of intersections of algebraic curves

**URL:** <https://discourse.julialang.org/t/using-intervalarithmetic-to-find-the-number-of-intersections-of-algebraic-curves/123740>\
**Category:** General Usage\
**Created:** [December 12, 2024, 7:35am UTC](https://discourse.julialang.org/t/using-intervalarithmetic-to-find-the-number-of-intersections-of-algebraic-curves/123740 "2024-12-12T07:35:27Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![ij05](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ij05/32/209328_2.png) [@ij05](https://discourse.julialang.org/u/ij05)\
**Post date:** [December 12, 2024, 7:35am UTC](https://discourse.julialang.org/t/using-intervalarithmetic-to-find-the-number-of-intersections-of-algebraic-curves/123740/1 "2024-12-12T07:35:27Z")

</div>

I have two algebraic curves as the following  
\begin{equation} 2x^2+4x-3-y=0\quad(1) \end{equation}  
x^2+y^2-a=0\quad\qquad(2)  
Equation (2) is parameterized in terms of a. I am interested to obtain the number of intersections between curves (1) and (2) as the parameter a changes.  
I thought of formulating the problem as follows:  
If a has an initial interval of

> a=interval(-10,10);

Then what are the intervals where curves 1 and 2 have exactly four intersections? I have reviewed IntervalArithmatic and IntervalConstraintProgramming packages and not sure if I can find a solution to this. I would be deeply greatful to any pointers.  
Thanks in advance!