We saw that slicing a cone at various angles could produce c

We saw that slicing a cone at various angles could produce cross sections in the shape of a circle, ellipse, parabola or hyperbola. There are 3 other \"degenerate\" sections. Pick them from the choices below, and indicate how the cone must be sliced to produce each one. Remember, you can only make 1 cut!

Solution

a)

Make a cut parallel to axis of the cone passing through the vertex of the cone.

d)

Make a cut passing through the vertex tangent to the surface of the cone. This gives a line

e)

Make a cut through the vertex parallel to the base of the cone. This gives you a point which is the vertex of the cone.