Computing a point having distances from 2 points respectively I want to compute a point $p$ which has distances $d1$ and $d2$ from points $q1$ and $q2$ respectively.
As I wanted a general answer, I used Maxima inputting the following script ,
$solve($
$[sqrt((num1-x)^2+(num2-y)^2)=num3,$
$sqrt((num4-x)^2+(num5-y)^2)=num6]$
$,[x,y]);$
Where all variables of the format $num$_ were constants in my mind and $p=(x,y)$.
I expected an output like , x= ... ; y= ..... .
Though,the output was just an empty bracket $[]$.
Is the script mathematically wrong or lacking some information or
 just a problem of the software ,Maxima?
(*Optionally, I am glad if you let me know a script which works well.)
Thank you in advance.

As @AustinMohr noted, this problem has no solution in general case (i.e., for arbitrary values of the inputs). It will have a solution (there exists $p$) if and only if anyone of the following two conditions is satisfied:


*

*$\quad d_0=|q_1q_2|=d_1+d_2$,

*$\quad d_0=|d_1-d_2|$,

*$\quad d_0, d_1, d_2$ are the sides of  a triangle which is true iff $d_i\le s~\forall i=1,2,3; s=\text{ ``half-perimeter" }=\frac{d_0+d_1+d_2}{2}$
Case1: In this case $p$ is the (unique) lies inside $|q_1q_2|$ and is given by $p=\frac{d_2.q_1+d_1.q_2}{d_1+d_2}$.
Case2: In this case $p$ lies on the extended $|q_1q_2|$ and is given by $p=\frac{d_2.q_1-d_1.q_2}{d_2-d_1}$.
Case3: $p$ is the two intersecting points of the two circles $C_1(q_1,d_1)$ and $C_2(q_2,d_2)$.

Edit: Yes, $p$ is always the intersecting point(s) of the two circles $C_1(q_1,d_1)$ and $C_2(q_2,d_2)$. I think the result holds in higher dimensions as well. 
