Is this graph schetched right?

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In summary: It is figure 15.2.2.In summary, the conversation discusses a picture from a solutions manual that shows a hyperboloid of one sheet with a hole of radius 4 around the z-axis. It is questioned whether this is correct, as the hyperbola should cross the y-axis at y=+-4 but it appears to go all the way to the origin.
  • #1
hyper
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In the sollutions manual is this picture:
http://img7.imageshack.us/my.php?image=graph.png

But how can this be right? If you put x=0 or z=0, you are supposed to get hyperbolas in the yz-and xz-plane, but they are straight lines?

I think you will get a hyperbola in the yz-plane cause you get the equation y^2-16z^2=16, this can be written like (y^2)/4^2-z^2=1. Have I overlooked anything, or is the sollutions manual wrong here?
 
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  • #2
hyper said:
In the sollutions manual is this picture:
http://img7.imageshack.us/my.php?image=graph.png

But how can this be right? If you put x=0 or z=0, you are supposed to get hyperbolas in the yz-and xz-plane, but they are straight lines?

I think you will get a hyperbola in the yz-plane cause you get the equation y^2-16z^2=16, this can be written like (y^2)/4^2-z^2=1. Have I overlooked anything, or is the sollutions manual wrong here?

I'm not sure what your question is. Yes, if x= 0 you get a hyperbola in the yz-plane and similarly for y= 0. I don't know why you say "but they are straight lines". If you are saying they look like straight lines in the picture, that picture simply is large enough or detailed enough to tell. The figure is a "hyperboloid of two sheets".
 
  • #3
But look in the yz-plane, we are supposed to see the hyperbola y^2/(16)-z^2=1. The means it is supposed the cross the y-axis at y=+-4, but it goes all the way to the origin?
 
  • #4
I take back what I said before. That is a hyperboloid of one sheet and there is a "hole" of radius 4 around the z-axis. Where did you get that picture? It looks like it might be the graph of [itex]16z^2- x^2- y^2= 16[/math].
 
  • #5
Thank you. I got it from the sollutions manual from Thomas Calculus.
 

1. What is the purpose of sketching a graph?

Sketching a graph allows for a visual representation of data or a mathematical function. It helps to analyze and interpret relationships between variables and make predictions.

2. How do I know if my graph has been sketched correctly?

A correctly sketched graph should have a clear and accurate representation of the data or function, with properly labeled axes, appropriate scaling, and all points plotted correctly. The graph should also follow any specific guidelines or instructions given for the assignment.

3. Can I use a computer program to draw my graph?

Yes, there are many computer programs and software available for creating graphs. However, it is important to understand the underlying concepts of graphing and ensure that the program is accurately representing the data or function.

4. How can I improve my graphing skills?

Practice is key to improving graphing skills. It is also helpful to understand the different types of graphs and when to use them, as well as any relevant mathematical principles. Seeking feedback and guidance from a teacher or mentor can also be beneficial.

5. Are there any common mistakes to avoid when sketching a graph?

Some common mistakes to avoid when sketching a graph include not labeling the axes, using inappropriate scaling, not plotting all data points, and not following any given guidelines or instructions. It is also important to double-check for errors or typos before finalizing the graph.

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