Ok then, here's a tricky one.

**Undefdisfigure** · March 12th 2008, 12:10 AM

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.

**ThePerfectHacker** · March 12th 2008, 06:51 AM

Originally Posted by Undefdisfigure

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.

The distance from x-axis to $(x,y,z)$ is given by $\sqrt{y^2+z^2}$ . The distance from $(x,y,z)$ to yz-plane is given by $|x|$ . Thus, we want $\sqrt{x^2+y^2} = 2|x|$ . And this is a double cone because of the presence of an absolute value.

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