Math Is Fun Forum

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Graphing a Circle

Hello all,

I originally tried to graph a circle on my 'TI-89 GFX Calculator (possibly irrelevant)', but I was (and still am) unsuccessful in doing so.

I know the basic formula:

But the calculator will only accept equations in the form,

So I re-arranged the equation and solved for y:

I might have for instance

, but this is when I realise something is wrong: instead of graphing a circle with radius 3, the calculator goes ahead and creates a little semi-circumference (concave from beneath) resting on the y-axis.

I look over the equation carefully and realise that if x=(any more than r), then y is undefined. But how can this be?!?! All I did was re-arrange the equation to suit my stupid calculator and what was previously simple circle with radius of length 3 turns into an undefinable circle .

Can someone please tell me what a did wrong and how to draw a circle on my calculator, if it is even possible.

Oh, and if it is, please also tell me how to translate it along both axes.

Last edited by Toast (2006-11-29 23:08:01)

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Graphing a Circle

the reason youre only getting a semi circle, is that y = sqrt(r^2 - x^2) is only a functino for the top curve, for the whole circle, it needs to be +/- sqrt(r^2 - x^2) depending upon whether youre calculator allows a plus/minus sign, governs whether itll let you graph a full circle.

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The Beginning Of All Things To End.
The End Of All Things To Come.

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Graphing a Circle

hmm thanks,
I couldn't find the +/-, so I put in 2 equations, one positive and the other negative. I didn't get a circle though, but rather an oval shape, alot like an eyelid, and the graphs weren't joined at the x axis, but rather where both a little way up/down from it.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Graphing a Circle

The reason for the oval shape would be that your axes have different scales. So, it would be displaying -3<x<3 and -10<y<10, for example. As for it not joining up properly, the only reason I can think of for that is that it could have been an effect of the loss of accuracy because the calculator has to 'pixellate' the graph to display it.

Incidentally, if your calculator can draw paramatric graphs, then circles are much easier to draw like that.

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Why did the vector cross the road?
It wanted to be normal.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Graphing a Circle

Remember what your calculator asks for:

f =

They chose f for a reason.  f stands for function.  Remember the basic definition of a function is that it is well defined.  That is, for every given x value, there is at most 1 corresponding y value.

So given that basic definition, when graphing a single function, it is impossible to draw a circle.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Graphing a Circle

However, you can try parametric plotting, such as (5cos(t), 5sin(t)), where cos(t) and sin(t) are well defined as functions.

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X'(y-Xβ)=0

Joe Shmoe

Guest

Re: Graphing a Circle

you also asked hoew to translate the graph.

to move it left and right, you simply add the number left that you want to go to X, and the number up to the whole equasion.

ex.
you start with y=sqrt(r^2-x^2)

to move it left 3, you would have:
y=sqrt(r^2-(x+3)^2)

or right 3:
y=sqrt(r^2-(x-3)^2)

and up 3 looks like:
y=sqrt(r^2-x^2)+3

ect

Toast

Real Member

Registered: 2006-10-08

Posts: 1,321

Re: Graphing a Circle

Thanks Joe

Mandy Mayday

Member

Registered: 2006-11-29

Posts: 4

Re: Graphing a Circle

ooooooooooooooooooooooops,
always amazing to watch someone solve abstract stuff like this. How do you guys do that?????