Finding the equation of a hyperboloid

[RKOwens4]

Homework Statement

"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".)

Homework Equations

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

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.

 

[jegues]

Use

$$(\frac{x}{2})^{2} + (\frac{y}{4})^{2} - (\frac{z}{c})^{2} = 1$$

and simply subsistute your points where,

$$Z \neq 0$$

and from there you should be able to compute c.

Spoiler

$$c = \pm \frac{7}{\sqrt{3}} \approx \pm 4.041$$

 

[RKOwens4]

That's correct. Thanks!