A positively charged particle 1 is at the origin of a Cartesian coordinate system, and there are no other charged objects nearby. You need the electric field magnitude at the position \((3.00 \mathrm{~nm}, 4. 00 \mathrm{~nm})\) to be zero, so that no electric force is exerted on any charged object placed at that location.

(a) Make a plot of all positions where a single additional charged particle 2 (of arbitrary charge) could be placed to make the electric field magnitude zero at \((3.00 \mathrm{~nm}, 4. 00 \mathrm{~nm})\). Explain some of the key points of your graph.

(b) Where would you need to place particle 2 if it carried the same charge as particle 1 ?