Explanation- If the diameter of Q is 6, then we want to cut that in half to make radius. Half of 6 is 3 so, to make the radius of P we need to cut 3 in half which would be 1.5 and if the diameter is 2r, 2 times 1.5 equals 3.
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.