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

find the present age, 5 years however, a man's age will be 3times his son'...

5 years however, a man's age will be 3times his son's age and 5 years ago, he was 7 times as old as his son.    Find their present ages.

Solve 4 sin 2 ( t ) - 3 sin ( t /3)= 1, Solve 4 sin 2 ( t ) - 3 sin ( t /...

Solve 4 sin 2 ( t ) - 3 sin ( t /3)= 1 . Solution Before solving this equation let's solve clearly unrelated equation. 4x 2 - 3x = 1  ⇒ 4x 2 - 3x -1 = ( 4x + 1) ( x

Lognormal distribution, The Lognormal Distribution If ln(X) is a normal...

The Lognormal Distribution If ln(X) is a normally distributed random variable, then X is said to be a lognormal variable. If P1, P2, P3, ... are the prices of a scrip in per

Determine a particular solution to differential equation, Determine a parti...

Determine a particular solution for the subsequent differential equation. y′′ - 4 y′ -12 y = 3e5t + sin(2t) + te4t Solution This example is the purpose that we've been u

Fractions and equations and illustration, if Mr.Ibias oredered a rectangula...

if Mr.Ibias oredered a rectangular pizza and he wants 2/3 of the pizza to be pepperoni and 1/2 of the pizza with pineapple draw and label the pizza with toppings explain your think

Important formulas of functions , Important formulas d (a b )/ dx  = 0...

Important formulas d (a b )/ dx  = 0                              This is a constant d ( x n ) / dx = nx n -1                      Power Rule d (a x ) / dx = a x l

What is probability that a person selected at random eyes, If 65% of the po...

If 65% of the populations have black eyes, 25% have brown eyes and the remaining have blue eyes. What is the probability that a person selected at random has (i) Blue eyes (ii) Bro

Geometry, the segments shown could form a triangle

the segments shown could form a triangle

Example on eulers method, For the initial value problem y' + 2y = 2 - e ...

For the initial value problem y' + 2y = 2 - e -4t , y(0) = 1 By using Euler's Method along with a step size of h = 0.1 to get approximate values of the solution at t = 0.1, 0

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