Find an equation for the surface consisting of all points $P$ for which the distance from $P$ to the $x$-axis is two times the distance from $P$ to the $y z$-plane.
A) $2 x ^ { 2 } = y ^ { 2 } - 2 z ^ { 2 }$
B) $4 x ^ { 2 } = y ^ { 2 } + z ^ { 2 }$
C) $2 x ^ { 2 } = y ^ { 2 } + 2 z$
D) $x ^ { 2 } - y ^ { 2 } - z ^ { 2 } = 2$
E) $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 4$

Question

Quizplus · Accepted Answer

The distance from a point $P(x, y, z)$ to the $x$-axis is $\sqrt{y^2 + z^2}$, and the distance to the $yz$-plane is $|x|$. The equation $4x^2 = y^2 + z^2$ satisfies the condition that the distance to the $x$-axis is twice the distance to the $yz$-plane.

Find an Equation for the Surface Consisting of All Points PPP

Find an Equation for the Surface Consisting of All Points $P$