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Finding the equation of a hyperboloid

by RKOwens4
Tags: equation, hyperboloid
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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.
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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!


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