\ / \ / X / \ / \

If a slice is taken horizontally, then a circle occurs. Generic formula: x^{2}+y^{2}=r (radius)

\ / __ _\___/_ / \ \ / | | X \__/ / \ / \If a slice is taken obliquely through one of the two halves, an ellipse can be seen. Generic formula: ax

^{2}+by

^{2}=c

\ _/_ \__// _/\ / _____ X / \ / \ \_____/ / \ / \If a slice is taken parallel with one of the sides of the cone, a parabola occurs, which extends upwards to infinity. (sample formula: y=nx

^{2}+c)

\ / / | ^^ | \ / / | | X / \ / / X | | / / \ \__/ / \ / \If a slice is taken through both cones, a hyperbola occurs. (can't remember formula)

\ |/ \ / \ | \ / \ /| \_ _/ X | \_/ / \| / | _ / |\ _/ \_ / \ / \ / \This is a rectangular hyperbola with all angles tending to 45 degrees, due to the vertical line.