Geometry
# Conic Sections

$A=(0,16,32)$ and circular base with center $O=(0,16,0)$ is standing on the $xy$-plane such that the origin is an endpoint of a diameter of the circular base. If $\alpha$ is a plane which passes through both $A$ and $O,$ what is the area of the intersection between the cone and the plane $\alpha?$

In the above diagram, a right cone with vertex$O$ that is perpendicular to the axis of the cone. Suppose $\angle ABC=60^\circ$ and $\overline{MON}$ is a diameter of the circular cross section. If the shape cut by a plane containing $\overline{MON}$ and a point $D$ on the cone surface is a parabola, what is the value of $x$ in degrees?

The above diagram shows a portion of an infinite right cone and a circular cross section centered at