(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

[tex]2\sqrt{(x_p-x)^2+(y_p-0)^2+(z_p-0)^2}=\sqrt{(x_p-0)^2+(y_p-y)^2+(z_p-z)^2}[/tex]

I square both sides simplify and move over to one side yielding:

[tex]3(x_p^2)+(3y_p^2+2y_py-y^2)+(3z_p^2+2zz_p-z^2)=0[/tex]

from here my natural intuition says to complete the square or factor but you can't do either. Where did I go wrong?

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# Surface with specifications

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