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.

Thanks for contributing solution to rwandachamber.org Stack Exchange!

Please be sure to*answer the question*. Carry out details and share her research!

But *avoid* …

Use rwandachamber.orgJax to style equations. rwandachamber.orgJax reference.

See more: 7 August 1967: George Harrison Haight Ashbury, George Harrison Photo: George And Pattie

To find out more, view our tips on writing great answers.

article Your answer Discard

By click “Post her Answer”, you agree come our regards to service, privacy policy and cookie plan

## Not the price you're spring for? Browse other questions tagged multivariable-calculus or questioning your own question.

site style / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.21.40536

rwandachamber.orgematics ridge Exchange works best with JavaScript enabled

your privacy

By clicking “Accept every cookies”, friend agree stack Exchange deserve to store cookies on your machine and disclose information in accordance v our Cookie Policy.