Register to reply

Finding the equation of a hyperboloid

by RKOwens4
Tags: equation, hyperboloid
Share this thread:
RKOwens4
#1
Jul21-10, 06:56 PM
P: 33
1. The problem statement, all variables and given/known data

"Find the equation of the hyperboloid of one sheet passing through the points (+-2, 0, 0), (0, +-4, 0) and (+-4, 0, 7), (0, +-8, 7)."

(What I mean by "+-" is the plus sign with the minus sign below it, read "plus or minus".)

2. Relevant equations

Equation for a hyperboloid of one sheet: (x/a)^2 + (y/b)^2 - (z/c)^2 = 1.

3. The attempt at a solution

I'm able to get the first part of the equation figured out easily. I get (x/2)^2 + (y/4)^2 - (z/?)^2 = 1. But I can't figure out what to put for the denominator in the z part. I thought maybe square root of 7, but that's wrong. I also tried 7, but that's incorrect. I know this is a really minor thing to be posting a whole thread about, but I can't figure it out and if anyone could help, it'd be appreciated.
Phys.Org News Partner Science news on Phys.org
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
jegues
#2
Jul21-10, 07:27 PM
jegues's Avatar
P: 1,089
Use

[tex] (\frac{x}{2})^{2} + (\frac{y}{4})^{2} - (\frac{z}{c})^{2} = 1 [/tex]

and simply subsistute your points where,

[tex] Z \neq 0 [/tex]

and from there you should be able to compute c.

Spoiler
[tex] c = \pm \frac{7}{\sqrt{3}} \approx \pm 4.041[/tex]
RKOwens4
#3
Jul21-10, 07:48 PM
P: 33
That's correct. Thanks!


Register to reply

Related Discussions
Find the volumn of a hyperboloid... Calculus & Beyond Homework 9
Is this a hyperboloid? Calculus & Beyond Homework 19
Hyperboloid problem Calculus & Beyond Homework 1
Area of hyperboloid Calculus 6