Hyperbolic paraboloid- three dimensional space, Mathematics

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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.

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