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

Quantitative, A lobster catcher spends $12 500 per month to maintain a lobs...

A lobster catcher spends $12 500 per month to maintain a lobster boat. He plans to catch an average of 20 days per month during lobster season. For each day, he must allow approx

Constants of integration, CONSTANTS OF INTEGRATION Under this section w...

CONSTANTS OF INTEGRATION Under this section we require to address a couple of sections about the constant of integration. During most calculus class we play pretty quick and lo

High dimensions, List the five most important things you learned about high...

List the five most important things you learned about high dimensions.

Rectilinear figure, In a parallelogram ABCD AB=20cm and AD=12cm.The bisecto...

In a parallelogram ABCD AB=20cm and AD=12cm.The bisector of angle A meets DC at E and BC produced at F.Find the length of CF.

Find final position of point by rotation -translation matric, Question: ...

Question: A point in 3D is first rotated anticlockwise by 45 degrees about x axis,then translated along y axis by 2 units.Find the final position of the point if its initial po

Differential equations and group methods, solve the differential equation ...

solve the differential equation dy/dx=f(y)x^n+g(y)x^m by finding a one-parameter group leaving it invariant

Generic rectangles and greatest common factors, miaty and yesenia have a gr...

miaty and yesenia have a group of base ten blocks.Misty has six more than yesnia. Yesenia''s blocks repersent 17 together they have 22 blocks,and the total of blocks repersent 85.

Green function, greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t...

greens function for x''''=0, x(1)=0, x''(0)+x''(1)=0 is G(t,s)= {1-s for t or equal to s

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