Question

Find the equation of the surface that is the set of all points whose absolute value of the difference of their distances from the points (2,0,0) and (-2,0,0) equals 6
I'm having trouble understanding the question maybe because of the wording. Idk, can someone clear it up for me?

Answer 1

its a definition of something :) (Hint :- from conic )

Answer 2

I'm sorry, I dont understand. I thought it had to do something with the distance formula. Am I wrong?

Answer 3

Since there is no yz plane.

Answer 4

\[| \sqrt{(x-2)^2 +y^2 +z^2} - \sqrt{(x+2)^2 +y^2 +z^2}| = 6\]
\[|u| = \sqrt{u^2}\]
\[(\sqrt{(x-2)^2 +y^2 +z^2} - \sqrt{(x+2)^2 +y^2 +z^2})^2 = 36\]

Answer 5

Ahh, Okay I was on the right track after all but the wording would throw me off. Thank you so much!

Answer 6

another approach , this is the def of hyperbola :)

Answer 7

Got it! Thanks! :)

Answer 8

wait actually its an ellipsoid

http://www.wolframalpha.com/input/?i=%28sqrt%28%28x-2%29%5E2+%2By%5E2+%2Bz%5E2%29+-+sqrt%28%28x%2B2%29%5E2+%2By%5E2+%2Bz%5E2%29%29%5E2+%3D+36