uncover an equation for the surface with all points which room equidistant of $(-1,0,0)$ and also the plane $x=1$. Draw the surface.

You are watching: Find an equation for the surface consisting of all points that are equidistant from the point

First, this is the graph I"ve depicted:

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Some concepts to find such equation and also the equivalent graph because that the surface?


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The distance from $(x,y,z)$ to the aircraft is just $|x-1|$, and the street from $(x,y,z)$ come $(-1,0,0)$ is $sqrt(x+1)^2+y^2+z^2$. Setup the 2 equal to eah other, us get

$$(x-1)^2 = (x+1)^2 + y^2 + z^2$$$$-4x = y^2 + z^2$$$$x = -frac14(y^2+z^2)$$


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If $z$ is not considered standard a 2D meaning of parabola deserve to be obtained by setup equal ranges as:

$$x = -fracy^24 $$

So through z thought about it i do not care a 3D generalized surface of transformation as a paraboloid rotated around $x$ axis vertically up :

$$ (x,y,z) = (-2,2,2)$$

$$x = -fracy^2+z^24 $$

$ yz $ airplane is horizontal, $x$ axis is vertical as shown.

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