As title says, how does one find an equation for the surface consisting of all points $P$ for which the distance from $P$ to the x-axis is three times the distance from $P$ to the $yz$-plane?
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$\begingroup$ What have you tried? For instance, suppose the $y$ and $z$ coordinates are given; what are the possible values for the $x$ coordinate. $\endgroup$– Karl KroningfeldCommented Sep 9, 2013 at 7:51
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2 Answers
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Hint: Note that the distance from $(x,y,z)$ to the $yz$-plane is $|x|$, and the distance from $(x,y,z)$ to the $x$-axis is $\sqrt{y^2+z^2}$.
answered Sep 9, 2013 at 7:34
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HINT
what is its locus if ratio $ x/y $ is constant and you rotate it on x-axis?
answered Nov 1, 2015 at 15:10