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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! Tags circles, issues Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post math_sooper_noob Abstract Algebra 1 October 27th, 2012 12:39 PM CherryPi Calculus 10 April 21st, 2012 10:23 PM Brightstar Geometry 3 January 19th, 2012 12:39 PM raiseit Math Events 1 June 1st, 2010 01:38 AM

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