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

Triangles, In a triangle ABC, D &E is a are points on AB & AC ,if the one s...

In a triangle ABC, D &E is a are points on AB & AC ,if the one side of a triangle is 4cm & another side is 5 cm find that the ar(triangleABC):ar(BCDE)

Measurement story problem, Seth has a pet goldfish. When he got his goldfis...

Seth has a pet goldfish. When he got his goldfish , it was only 5 centimeters long . Now it has grown to be 92 millimeters long. How many millimeters has the goldfish grown since

E is irrational, If e were rational, then e = n/m for some positive integer...

If e were rational, then e = n/m for some positive integers m, n. So then 1/e = m/n. But the series expansion for 1/e is 1/e = 1 - 1/1! + 1/2! - 1/3! + ... Call the first n v

Topological spease, let X be a nonempty set. let x belong to X. show that t...

let X be a nonempty set. let x belong to X. show that the collection l={ union subset of X : union = empty or belong U

Determine the conditional probability, Consider a class of 55 students. The...

Consider a class of 55 students. The student names are placed in a hat and 3 names are randomly drawn without replacement. a) If the first person drawn was named the class presi

Solving whole number riddles, What is the answer for I am greater than 30 a...

What is the answer for I am greater than 30 and less than 40. The sum of my digits is less than 5.

.gradient, Draw the graph of y=x^2-4x from x=-1 to x=5.use the scale of 2cm...

Draw the graph of y=x^2-4x from x=-1 to x=5.use the scale of 2cm on the x axis and 1cm on the y axis.Estimate the gradient at point:x=4, x=2 and x=0

Geometric applications to the cross product, Geometric Applications to the ...

Geometric Applications to the Cross Product There are a so many geometric applications to the cross product also.  Assume we have three vectors a → , b → and c → and we make

Example of exponential smoothing, Example of Exponential Smoothing ...

Example of Exponential Smoothing By using the previous example and smoothing constant 0.3 generate monthly forecasts Months Sales Forecast

Probability distributions, Probability Distributions Since the value of...

Probability Distributions Since the value of a random variable cannot be predicted accurately, by convention, probabilities are assigned to all the likely values that the varia

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