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:

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

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)\$\$

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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