Ok, I am stuck on this hyperboloid equation.

Find the equation of the hyperboloid of one sheet passing through the points and .

I know the general equation for the single sheet hyperboloid which is :
$\displaystyle (x/a)^2+(y/b)^2=(z/c)^2+1$

I have found (a) and (b) in the above equation, but how do I find (c)?

Thanks!!

2. Originally Posted by Esc
Ok, I am stuck on this hyperboloid equation.

Find the equation of the hyperboloid of one sheet passing through the points and .

I know the general equation for the single sheet hyperboloid which is :
$\displaystyle (x/a)^2+(y/b)^2=(z/c)^2+1$

I have found (a) and (b) in the above equation, but how do I find (c)?

Thanks!!
Just substitute in one of the points with z = 8. For instance, using (12, 0, 8):

$\displaystyle \left ( \frac{12}{a} \right ) ^2 = \left ( \frac{8}{c} \right ) ^2 + 1$

$\displaystyle \frac{144}{a^2} = \frac{64}{c^2} + 1$

$\displaystyle \frac{144}{a^2} - 1 = \frac{64}{c^2}$

$\displaystyle c^2 \left ( \frac{144}{a^2} - 1 \right ) = 64$

$\displaystyle c^2 = \frac{64}{ \frac{144}{a^2} - 1}$

3. Thank you so much for your help!!!!!