Answer:
Explanation:
The 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 can be found by using the distance formula in three dimensions.
Let (x, y, z) be a point P on the surface. The distance from P to the x-axis is |x|, and the distance from P to the yz-plane is sqrt(y^2 + z^2). Setting these two distances equal and solving for x, we get:
|x| = 2 * sqrt(y^2 + z^2)
x = 2 * sqrt(y^2 + z^2) if x >= 0
x = -2 * sqrt(y^2 + z^2) if x < 0
This is the equation for a hyperboloid of one sheet. The hyperboloid of one sheet is a three-dimensional surface with two connected components that are mirror images of each other across the x-axis.