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Finding the equation of a hyperboloid 
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#1
Jul2110, 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. 


#2
Jul2110, 07:27 PM

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]



#3
Jul2110, 07:48 PM

P: 33

That's correct. Thanks!



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