The Equation of a Cone

Date: 9/14/95 at 12:44:8
From: Anonymous
Subject: Equation of the cone

I would like to know the equation of the CONE.

For example I know that the sphere is

  (X-h)^2 + (Y-k)^2 + (Z-n)^2 = R^2

where (h,k,n) is the center, and the symbol ^ means elevation to a power.

Thank you for your help.

Luca M.

Date: 9/14/95 at 21:2:0
From: Doctor Ken
Subject: Re: Equation of the cone

Hello!

The equation of the cone can be thought of as a cylinder that we multiply
by z to achieve the narrowing effect.  Since a cylinder has equation like
x^2 + y^2 = 1   [it's in 3 coordinates, (x,y,z)], the cone has equation
x^2 + y^2 = z^2: that gives us a circle of radius z at height z.

In general, the formula (x-a)^2 + (y-b)^2 = ((z-c)R)^2  will be a cone whose
vertex is at (a,b,c) and which opens in the z direction.

- Doctor Ken,  The Geometry Forum