Question

Find an equation for the surface consisting of all points p for which the distance from p to the x-axis is 5 times the distance from p to the yz-plane.

Answer 1

Distance from P to the x-axis = 2x distance from P to the yz-plane 

Distance to the x-axis of a point P=(x,y,z) is (y^2+z^2)^1/2 
Distance to the yz-plane of a point P=(x,y,z) is x 

So your equation is: 
(y^2+z^2)^1/2 = 2x 
=> y^2 + z^2 = 4x^2 
=> y^2 + z^2 - 4x^2 = 0 

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