Hyperbolic paraboloid- three dimensional space, Mathematics

Assignment Help:

Hyperbolic Paraboloid- Three Dimensional Space

The equation which is given here is the equation of a hyperbolic paraboloid.

x2 / a2 - y2 / b2 = z/c

Here is a diagram of a typical hyperbolic paraboloid.

2339_Hyperbolic Paraboloid- Three Dimensional Space 1.png

These types of graphs are vaguely saddle shaped and like with the elliptic paraoloid the sign of c will find out the direction in which the surface "opens up".  The graph above is displayed for c positive.

Along with the both of the types of paraboloids discussed above the surface can be simply moved up or down by adding or subtracting a constant from the left side. 

For example 

Z = - x2 - y2 + 6

is an elliptic paraboloid which opens downward (be careful, the "-" is on the x and y instead of the z) and begins at z = 6 in place of of z = 0.

Now the below are a couple of quick sketches of this surface.

155_Hyperbolic Paraboloid- Three Dimensional Space 2.png

Notice that we have given two forms of the diagram here. The diagram on the right has the standard set of axes but it is hard to see the numbers on the axis.The diagram on the left has been "boxed" and this makes it easier to see the numbers to provide a sense of perspective to the sketch. So many sketches that actually include numbers on the axis system we will provide both sketches to help get a feel for what the diagram looks like.


Related Discussions:- Hyperbolic paraboloid- three dimensional space

Oscar sold 2 glasses of milk for each 5 sodas he sold, Oscar sold 2 glasses...

Oscar sold 2 glasses of milk for each 5 sodas he sold. If he sold 10 glasses of milk, how many sodas did he sell? Set up a proportion along with milk/soda = 2/5 = 10x. Cross mu

Determine the mean of given question, Q . Mrs. Cooper asked her math class ...

Q . Mrs. Cooper asked her math class to keep track of their own grade. Michael, one of the students, lost his assignments, but he remembered the grades of 6 out of 8 assignments:

Multiple integrals, how to convert double integral into polar coordinates a...

how to convert double integral into polar coordinates and change the limits of integration

Fractions, A car travels 283 1/km in 4 2/3 hours .How far does it go in 1 h...

A car travels 283 1/km in 4 2/3 hours .How far does it go in 1 hour?

How far did the ?rst arrow goes, From a fixed point directly in front of th...

From a fixed point directly in front of the center of a bull's eye, Kim aims two arrows at the bull's eye. The first arrow nicks one point on the edge of the bull's eye; the second

Squeeze theorem (sandwich theorem and the pinching theorem), Squeeze Theore...

Squeeze Theorem (Sandwich Theorem and the Pinching Theorem) Assume that for all x on [a, b] (except possibly at x = c ) we have,                                 f ( x )≤ h (

Compute the total and annual return on the investment, 1. Calculate the ann...

1. Calculate the annual interest that you will receive on the described bond-A $500 Treasury bond with a current yield of 4 .2% that is quoted at 106 points? 2. Compute the tota

Geometry, calculate the area of a trapezoid with height 8cm base 18cm and 9...

calculate the area of a trapezoid with height 8cm base 18cm and 9cm

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd