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Math Help - Quadric Surfaces

  1. #1
    Esc
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    Quadric Surfaces

    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 :
    (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!!
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  2. #2
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    Quote Originally Posted by Esc View Post
    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 :
    (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):

    \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}
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  3. #3
    Esc
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    Thank you so much for your help!!!!!
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