Locating a radar in a plane > Given two located targets at $(x, y)=(- 2.0)$ and $(x, y)=(2,0)$. A radar, located in an unknown location of the $XY$ plane, and sends a pulse and in return receives pulses from the two targets. Between the two pulses received, there is a lag time of $2/c$ seconds, where $c$ is the speed of light. What is the locus of possible positions of the radar? The travel time round-trip of a pulse between the radar and target is $2d/c$, where $d$ is the distance between the radar and the target. My attempt: Let us denote the first target $A$ et and the second $B$ I compute the between the radar and the target $d=\sqrt{(x_r+2)^2+y_r^2}$ where $\text{Radar}(x_r,y_r)$, I have also the vector $\overrightarrow{AB}=(4,0)$ and the equation of the plane in the form $ax+by+cz+d=0$, here we have $ax+by+d=0$. In fact my problem is I don't know where I am going. Any hint (please) on what I should do is welcome.

The condition implies that the difference between distances from the radar to the two targets is $$\frac{1}{2}\times\text{roundtrip time delay}\times\text{speed}=\frac{1}{2}\times\frac{2}{c}\times c=1$$ The locus of such points is a hyperbola with foci = targets.

You can also see that analytically by writing the equation $d_A=1+d_B$ (where $d_x=\text{dist}(\text{radar},x)$) and squaring it twice to get rid of roots.