# Math Help - Ok then, here's a tricky one.

1. ## Ok 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.

2. 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.