Balancing forces on charged balls hanging on strings

[orbital_laser]

Homework Statement

A small ball having a positive charge q1 hangs by an insulating thread. A second ball with a negative charge q2=-q1 is placed at a horizontal distance a to the right of the first, this distance being very large compared with the diameter of the ball.
a. Show in a diagram all of the forces on the hanging ball in its final equilibrium position.
b. You are given a 3rd ball having a positive charge q3 = 2q1. Find at least 2 points at which this ball can be placed so that the first ball will hang vertically.

Relevant Equations

F = kq^2 / r^2

Answer says, 'any (x, y) satisfying 2(a^2)x = (x2 + y2)^(3/2)

 

[TSny]

Hello and welcome to PF!

In order to receive help, you should show some attempt at solving the problem. General guidelines for posting questions in the homework forums are given here
https://www.physicsforums.com/threads/guidelines-for-students-and-helpers.686781/Note items 4 and 8.

Even if you can't get very far, you can still describe your thoughts about the problem. Try to indicate what aspects of the problem are giving you difficulty. Are you asking about both parts (a) and (b), or just part (b)?