Hyperboloids and Ellipsoids

hyperboloid of one sheet

hyperboloid of two sheets

ellipsoid

semimajor and semiminor axes

a

0.25

b

0.25

c

0.25

axes

translate model along axes

x

0

y

0

z

0

reset

This Demonstration shows hyperboloids of one and two sheets as well as ellipsoids. When modeling ellipsoids, make the

a

,

b

, and

c

values equal to form a sphere.

The equation for the hyperboloid of one sheet is

2

(x-h)

2

a

+

2

(y-k)

2

b

-

2

(z-l)

2

c

=1

. The equation for the hyperboloid of two sheets is

2

(x-h)

2

a

+

2

(y-k)

2

b

-

2

(z-l)

2

c

=-1

, and the equation of the ellipsoid is

2

(x-h)

2

a

+

2

(y-k)

2

b

+

2

(z-l)

2

c

=1

.