My Math Forum ISSUES with circles...

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 September 9th, 2010, 03:02 PM #1 Member   Joined: Sep 2010 Posts: 32 Thanks: 0 ISSUES with circles... A circle in R^3, ie 3D space is written as: f(x,y)= x^2+ y^2 If we want to draw level curves we give the function different values of C, for example: C= 1 --> x^2+ y^2 = 1, This will give us a circle with the center in (0,0) and the radius = sqrt(1)=1 BUT what changes when we have x^2+ 4y^2 What does the 4 change, does it change the centre of the circle? Also, how should one sketch x^2+y^2+z^2 < 5?? An answe to any of the two questions is highly appreciated... Please help me!
September 9th, 2010, 03:21 PM   #2
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Re: ISSUES with circles...

Quote:
 Originally Posted by tinyone What does the 4 change, does it change the centre of the circle?
It turns the circle into an ellipse.

September 10th, 2010, 01:29 PM   #3
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Re: ISSUES with circles...

Quote:
 Originally Posted by tinyone A circle in R^3, ie 3D space is written as: f(x,y)= x^2+ y^2
Wrong. If you have 3D space, you have a function f(x,y,z). You have R^3 -> R^2. z is not used in the function but it does exist.

Quote:
 If we want to draw level curves we give the function different values of C, for example: C= 1 --> x^2+ y^2 = 1, This will give us a circle with the center in (0,0) and the radius = sqrt(1)=1
wrong, see above.
Quote:
 BUT what changes when we have x^2+ 4y^2 What does the 4 change, does it change the centre of the circle?
See the last post.

Quote:
 Also, how should one sketch x^2+y^2+z^2 < 5??
Now we are going from 3D to 3D since you do not determine it to a fixed number ... this is an open sphere, with a volume.
You seem to misunderstand functions. Think about what R^n -> R^m means, as a hint.

 September 10th, 2010, 05:43 PM #4 Member   Joined: Sep 2010 Posts: 32 Thanks: 0 Re: ISSUES with circles... ok good point but is it not possible to draw level curves for f(x,y)= x^2+ y^2 by assigning it different constants?
September 11th, 2010, 02:42 AM   #5
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Re: ISSUES with circles...

Quote:
 Originally Posted by tinyone . . . but is it not possible to draw level curves for f(x,y)= x^2+ y^2 by assigning it different constants?
Yes. If z = f(x, y) = x^2 + y^2 you have an elliptic paraboloid.

Quote:
 Originally Posted by tinyone x^2+ 4y^2
In space, this is an elliptic paraboloid. In the plane it is an ellipse.

 September 11th, 2010, 08:00 AM #6 Member   Joined: Sep 2010 Posts: 32 Thanks: 0 Re: ISSUES with circles... Thank you very much greg1313, that cleared up a lot!

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