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
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