• May 8th 2008, 11:01 AM
Esc
Ok, I am stuck on this hyperboloid equation.

Find the equation of the hyperboloid of one sheet passing through the points https://webwork.math.lsu.edu/webwork...6d7e3ae161.png and https://webwork.math.lsu.edu/webwork...935f219a21.png.

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

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

Thanks!!(Hi)
• May 8th 2008, 11:13 AM
icemanfan
Quote:

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 https://webwork.math.lsu.edu/webwork...6d7e3ae161.png and https://webwork.math.lsu.edu/webwork...935f219a21.png.

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

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

Thanks!!(Hi)

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

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

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

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

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

$c^2 = \frac{64}{ \frac{144}{a^2} - 1}$
• May 9th 2008, 12:00 AM
Esc
Thank you so much for your help!!!!! (Clapping)(Hi)