Homework Help: Surfaces of 3 Variable Question

1. Sep 14, 2011

stratusfactio

1. The problem statement, all variables and given/known data

A cone C, with height I and radius I, has its base in
the xz-plane and its vertex on the positive y-axis. Find a
function g(x, y, z) such that C is part of the level surface
g(x, y, z) = 0.

2. Relevant equations
What would be the formula for the cone such that the base of the cone is lying on the xz-plane and the vertex is on the y-axis?

3. The attempt at a solution
We know that the formula for a cone is $$x^2+y^2-z^2$$, but we don't know where to go from there to get the formula for the description above.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 14, 2011

Dick

x^2+y^2-z^2 has it's vertex at (0,0,0) and it's axis along the z axis. Your cone has it's vertex at (0,I,0) and axis along the y axis. You'll need to interchange some variables to get the axis right and then shift the vertex up to (0,I,0). Sketch some graphs.