Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to the yz-plane. Identify the surface.

I get that the surface is a cone, but maybe my graph is off.

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- Mar 12th 2008, 12:10 AMUndefdisfigureOk then, here's a tricky one.
Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to the yz-plane. Identify the surface.

I get that the surface is a cone, but maybe my graph is off. - Mar 12th 2008, 06:51 AMThePerfectHacker
The distance from x-axis to $\displaystyle (x,y,z)$ is given by $\displaystyle \sqrt{y^2+z^2}$. The distance from $\displaystyle (x,y,z)$ to yz-plane is given by $\displaystyle |x|$. Thus, we want $\displaystyle \sqrt{x^2+y^2} = 2|x|$. And this is a double cone because of the presence of an absolute value.