The trace of the hyperbolic paraboloid.

[Win_odd Dhamnekar]

Hello,
How to find the trace of hyperbolic paraboloid \(\frac {x^2}{a^2}-\frac{y^2}{b^2}=\frac{z}{c}\)in the xy-plane, yz-plane, xz-plane where x > 0, y > 0, z >0? If c < 0, how would you change your answer?



If any member knows correct answer to this question may reply.

 

[Deleted member 4993]

Hello,
How to find the trace of hyperbolic paraboloid \(\frac {x^2}{a^2}-\frac{y^2}{b^2}=\frac{z}{c}\)in the xy-plane, yz-plane, xz-plane where x > 0, y > 0, z >0? If c < 0, how would you change your answer?

View attachment 19261

If any member knows correct answer to this question may reply.

In xy plane what is the value of "z" for any curve? So the trace of the surface

\(\displaystyle \frac {x^2}{a^2}-\frac{y^2}{b^2}=\frac{z}{c} \ \) would be (on x-y plane)

\(\displaystyle \frac {x^2}{a^2}-\frac{y^2}{b^2}=\frac{0}{c} \ \)

\(\displaystyle \frac {x^2}{a^2}-\frac{y^2}{b^2}=0 \ \)

continue....