Quadric Surfaces Bold text
1. Here is the general equation of an ellipsoid
x^2/a^2+y^2/b^2+z^2/c^2 = 1
An ellipse is a generalization of a circle, and ellipsoid is a generalization of a sphere. Planet earth is not a true sphere. It is an ellipsoid. You will know if it is an ellipsoid if it is wider than it is taller.
2. Here is the general equation of a cone
x^2/a^2 +y^2/b^2 = z^2/c^2
A cone is a shape that tapers smoothly from a base to a point called the apex or vertex.
3. Here is the general equation of a cylinder
x^/a^2+y^b^2= 1
A cylinder is one of the most basic curvilinear geometric shapes, the surface formed by the points at a fixed distance from a given line segment.
4. Here is the equation of a hyperboloid of one sheet
x^2/a^2+y^2/b^2-z^2/c^2=1
The variable with the negative in front of it will give the axis along which the graph is centered.
5. Here is the equation of a hyperboloid on two sheets
-x^2/a^2-y^2/b^2 + z^2/c^2 = 1
The only difference between the hyperboloid of one sheet and the hyperboloid of two sheets is the signs in front of the variables. They are exactly the opposite signs.
Insert non-formatted text here 6. Here is the equation of a elliptic paraboloid
x^2/a^2 +y^2/b^2 = z/c
As with cylinders this has a cross section of an ellipse and if it will have a cross section of a circle. When we deal with these we’ll generally be dealing with the kind that have a circle for a cross section.
7. Here is the equation of a Hyperboloic Paraboloid
x^2/a^2 -y^2/b^2 = z/c
These graphs are vaguely saddle shaped and as with the elliptic paraoloid the sign of c will determine the direction in which the surface “opens up”. The Quadric Surfaces are sometimes not l
Wilson Williams
