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I have the equation for a hyperbolic paraboloid in $x$, $y$, and $z$:

$$\frac{z}{c} = \frac{x^2}{a^2} + \frac{y^2}{b^2}$$

I also have the parametric equations for the same parabaloid:

$$x = a u \cos v \qquad y = a u \sin v \qquad z = u^2$$

Can someone show me algebraically how to go from the standard to the parametric forms?

I can't figure out where the missing $c$ went and I need to know because I'm trying to use the equations in writing a computer program, in which I need to input values for $a$, $b$, and $c$.

Apologies for not using the math formatting code, I'm still figuring it out. Thanks in advance!

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I think you should have $y=bu\sin v$ and $z=cu^2$. –  user12477 Jul 3 '12 at 21:05
    
I did some formatting, but no fixing. I'll let you address @user12477's suggestions (with which I agree). –  Blue Jul 3 '12 at 21:09
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