Fun with Math!: Hyperboloid of two sheets

A hyperboloid of two sheets is a type of quadric surfaces that carries one of the equations below

$-\frac{x^2}{a^2}-\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ $-\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$ $\frac{x^2}{a^2}-\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$
if it is centered at the origin. If it is shifted to be centered at (h, k, l), then its equation will be one of the below: $-\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}+\frac{(z-l)^2}{c^2}=1$ $-\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}-\frac{(z-l)^2}{c^2}=1$ $\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}-\frac{(z-l)^2}{c^2}=1$
The graph below consists all the graphs mentioned above. The center will appear when you choose the type of graph. Tick on one box at a time to avoid confusion. Do un-tick the box first before choosing another box. Check on the following matters when you play around with the graph:

What is the axis of the graph?
What are the intercepts?
How do the value of a, b, c affect the graph?

If you want to rotate freely on the graph, please click here.

Betty, created with GeoGebra and Thomas Calculus, Pearson.

Fun with Math!

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Thursday, May 14, 2020

Hyperboloid of two sheets

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