Center.java

    public static PlasmaPoint2D[] possibleCenters(PlasmaPoint2D pointa, PlasmaPoint2D pointb, double radius) {
        double x1 = pointa.getX();
        double x2 = pointb.getX();
        double y1 = pointa.getY();
        double y2 = pointb.getY();
        double r = radius;

        double ca = (x1 * x1) + (y1 * y1) - (x2 * x2) - (y2 * y2);
        double x3 = x1 - x2;
        double y3 = y1 - y2;
        double cy = (ca/(2 * y3)) - y1;

        double a = ((x3 * x3) + (y3 * y3)) / (y3 * y3);
        double b = ((2 * x1) - (2 * (cy) * x3/y3));
        double c = ((x1 * x1) + (cy * cy) - (r * r));

        double[] roots;
        double denominator = 2 * a;
        double bNumerator = -b;
        double underSquare = (b * b) - (4 * a * c);
        if (underSquare < 0 || denominator == 0) {
            roots = new double[0];
        } else {
            double sqrt = Math.sqrt(underSquare);
            roots = new double[]{(bNumerator + sqrt) / denominator, (bNumerator - sqrt) / denominator};
        }

        PlasmaPoint2D[] points = new PlasmaPoint2D[roots.length];
        for (int i = 0; i < roots.length; i++) {
            double x = roots[i];
            double y = -(x3/y3) * x + (c/(2 * y3));
            points[i] = new PlasmaPoint2D(x, y);
        }

        return points;
    }

This approach will not work when points lie in the same y coordinate. It will lead to y3 == 0 in line 10 and 0 division errors in lines 11, 13, 14. There are alternatives implementation in https://rosettacode.org/wiki/Circles_of_given_radius_through_two_points.