http://www.ck12.org Chapter 9. Conics
As you tilt the plane even further and the slope of the plane equals the slope of the cone edge you produce a
parabola. Since the slopes are equal, a parabola only intersects one of the cones.
Lastly, if you make the plane steeper still, the plane ends up intersecting both the lower cone and the upper cone
creating the two parts of a hyperbola.
The intersection of three dimensional objects in three dimensional space to produce two dimensional graphs is quite
challenging. In practice, the knowledge of where conics come from is not widely used. It will be more important
for you to be able to manipulate an equation into standard form and graph it in a regular coordinate plane. The
regular form of a conic is:
Ax^2 +Bxy+Cy^2 +Dx+Ey+F= 0