If it passes through zero, then that could be a first point (0, 0). If you have the function of the curve, you can get other points by plugging in numbers for x and solving for y, giving you more...
Construct perpendicular bisectors for 2 of the segments formed from 3 points. Note: this will be the center of the circle that has all three points on it's circumference.
In spherical geometry we look at the globe as the sphere
S^2. Any plane intersecting the sphere will create a great circle. Now if you take any point on the globe and reflect it across that...