intersection - How to check if two curves intersect in mathematica -


i have set of parametric curves , reference curve, , want see ones intersect reference curve.

for example, let's function1's parametric curves , function 2 reference curve.

function1[x_,a_]:=x^2+a function2[x]:=1

how can know function1 intersect function2 "in clean way". tried using findroot:

in:= findroot[function1[x, 1] == function2[x], {x, 1}] out= {x -> 1.}

it works case, in case not work, mathematica provides me absurd value, error message.

in[485]:= findroot[function1[x, 4] == function2[x], {x, 1}]  "during evaluation of in[485]:= findroot::lstol: line search decreased step size within tolerance specified accuracygoal , precisiongoal unable find   sufficient decrease in merit function. may need more machineprecision digits of working precision meet these tolerances. >>"  out[485]= {x -> 3.09187*10^-6}

instead of having absurd value (in case not intersect) or exact value (in case intersect), "true" or "false" statement. idea how implement this?


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