I'm trying to solve for $x$ and $y$ in the following system of of equations:
$$((x-m)^2+(y-j)^2)(x-m)^2=((x-k)^2+(y-l)^2)(x-k)^2$$
$$((x-m)^2+(y-j)^2)(y-j)^2=((x-k)^2+(y-l)^2)(y-l)^2$$
I've tried plugging it in to WolframAlpha as such:
Solve$[{(((x-m)^2)+((y-j)^2))((x-m)^2)=(((x-k)^2)+((y-l)^2))((x-k)^2), (((x-m)^2)+((y-j)^2))((y-j)^2)=(((x-k)^2)+((y-l)^2))((y-l)^2)}, {x,y}]$
When I plug that in, it just processes for a little and then returns the page with no answer.
If I substitute constants for $m$,$j$,$k$,$l$ $(m=2,j=2,k=10,l=10)$, it works perfectly and returns $x=6$ and $y=6$ (which is the right answer). I feel like if it can solve it using numbers, it should be able to solve it for unspecified constants.
Does anyone have any insight as to how I should solve this$?$
Thanks!
Assuming that no terms vanish, observe that
$$\frac{(y-j)^2}{(x-m)^2} = \frac{(y-l)^2}{(x-k)^2}$$ Call it $\lambda$. Then,
$$(x - m)^4(1 + \lambda^2) = (x - k)^4(1 + \lambda^2)$$
That is,
$$(x-m)^4 = (x-k)^4$$
Can you take it from here?