You can get a circle by cutting horizontally and a hyperbola by cutting vertically. You can also get an ellipse and a parabola by cutting at an angle depending on whether the cut comes out the other side or not.
Here's why:
<span>Say the 5 people are A, B, C, D, E </span>
<span>A shakes hands w/ B C D E </span>
<span>B shakes w/ C D E </span>
<span>C with D E </span>
<span>D with E </span>
<span>That's 10</span>
Multiply equation II by 2 and then add up the equations.
The equation of a cricle is

h being the x coordinate of the given point and k being the y coordinate of the given point (r also being the radius).
Now we have to plug the points into the equation

now just simplify the the equation