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A stupid question. - HSN forum

A stupid question.

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#1Sammie

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Posted 07 March 2007 - 05:12 PM

Ok ~ This is like the level C revision crap they had out and its a really stupid stupid questions I know but ~

Explain why x[squared] + y[squared] + 6x - 4y + 17 = 0 LOOKS like it represents a circle but in fact does not.

Is it because its = 0 and you cant get a circle with a radius of 0?
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#2Steve

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Posted 07 March 2007 - 06:11 PM

It is to do with the radius, but that equation doesn't mean the radius is zero.

You're given this in the exam: the circle with equation has centre and radius .

So for , we have and . So , and . This means the radius would be which isn't a real number. Hence the equation doesn't represent a circle.

And it's not a stupid question - there have been ones in the exam like it before!
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#3dfx

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Posted 07 March 2007 - 11:34 PM

Out of curiosity, would it represent a circle with radius 2i?

#4Steve

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Posted 08 March 2007 - 07:16 PM

QUOTE(dfx @ Mar 7 2007, 11:34 PM)
Out of curiosity, would it represent a circle with radius 2i?

Interesting. I'd say 'no'. The definition of a circle is 'the locus of points equidistant from a fixed point called the centre, where the common distance between the centre and each point in the locus is called the radius'.

So the idea of distance is key in defining what a circle is. Measuring distance is done using a 'metric', which is a function which assigns to two objects of a set a real number which is greater than (or equal to) zero (i.e. just some measurement of how far apart they are, in some sense). See Metric (Wikipedia) and Circle (Wikipedia).

Measuring a distance only makes sense, to me anyway, if you can say that something is 'closer' to something than something else. You can't do that if you measure distance in complex (non-real) numbers, since there is no notion of inequality.

I'm convinced!
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#5John

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Posted 08 March 2007 - 07:35 PM

My graphing calculator, returns no error, shows a graph of nothing. *shrugs*

#6Steve

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Posted 08 March 2007 - 08:01 PM

QUOTE(John @ Mar 8 2007, 07:35 PM)
My graphing calculator, returns no error, shows a graph of nothing. *shrugs*

Calculators aren't any sort of maths oracles!

The circle certainly doesn't exist in the plane, since each point in the plane has real coordinates. If anything it would exist in two-dimensional complex space, or four-dimensional real space (which your calculator certainly can't draw)!

But even still you need a way of measuring distance which allows you to say that something is close to something else - you cannot do this with imaginary numbers, e.g. has no meaning for .
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#7John

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Posted 08 March 2007 - 08:09 PM

Computer programmes should be though, but what should I expect, it was a Microsoft app lol

#8dfx

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Posted 09 March 2007 - 09:36 AM

QUOTE(Steve @ Mar 8 2007, 07:16 PM)
QUOTE(dfx @ Mar 7 2007, 11:34 PM)
Out of curiosity, would it represent a circle with radius 2i?

Interesting. I'd say 'no'.

I shall agree. Thanks.

#9Sammie

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Posted 09 March 2007 - 04:04 PM

Thanks guys ~ <333

And to let you all know ~ I passed the dreaded unit 2 Nab resit

*DANCES*

And considering I got 6% in the first sit and 8% in the prelim I did pretty damn well in a week xDD
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#10Nathan

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Posted 09 March 2007 - 06:52 PM

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