Warning: Illegal string offset 'html' in /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php on line 909

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 114

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 127

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 136

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 137

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 141
A stupid question. - HSN forum

Jump to content


A stupid question.


9 replies to this topic

#1 Sammie

    Top of the Class

  • Members
  • PipPipPipPipPip
  • 380 posts
  • Location:Glasgow
  • Interests:Stuff... mainly Fall Out Boy
  • Gender:Female

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?
"Crowds are won and lost and won again, but our hearts beat for the diehards"

#2 Steve

    Top of the Class

  • Admin
  • PipPipPipPipPip
  • 435 posts
  • Location:Edinburgh
  • Gender:Male

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 x^2+y^2+2gx+2fy+c=0 has centre (-g,-f) and radius \sqrt{g^2+f^2-c}.

So for x^2 + y^2 + 6x - 4y + 17 = 0, we have 2g=6 and 2f=-4. So g=3, f=-2 and c=17. This means the radius would be \sqrt{9+4-17}=\sqrt{-4} 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!
HSN contribute: Help the site grow!

Looking for a Maths tutor in West Lothian? Just PM me!

#3 dfx

    Fully Fledged Genius

  • Members
  • PipPipPipPipPipPipPip
  • 1,955 posts
  • Gender:Male

Posted 07 March 2007 - 11:34 PM

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

#4 Steve

    Top of the Class

  • Admin
  • PipPipPipPipPip
  • 435 posts
  • Location:Edinburgh
  • Gender:Male

Posted 08 March 2007 - 07:16 PM

QUOTE(dfx @ Mar 7 2007, 11:34 PM) View Post
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!
HSN contribute: Help the site grow!

Looking for a Maths tutor in West Lothian? Just PM me!

#5 John

    HSN Legend

  • Members
  • PipPipPipPipPipPipPipPip
  • 2,713 posts
  • Location:In a Peripheral Estate in Glasgow
  • Interests:First the boring stuff:<br /><br />2004 Results:<br /><br />Highers:<br /><br />Computing A<br />Craft and Design A<br />Physics A<br />Administration A<br />English A<br />Maths A<br />Modern Studies A<br />French A<br /><br />2005 Results:<br /><br />Advanced Highers:<br />Computing A<br />Physics A<br />Maths A<br />Modern Studies A<br />English A<br /><br />2006 Results:<br /><br />Advanced Highers(All Crashed):<br />Chemistry A<br />Biology A<br />Business Managemnt A<br /><br />Aren't I marvellous?
  • Gender:Male

Posted 08 March 2007 - 07:35 PM

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

#6 Steve

    Top of the Class

  • Admin
  • PipPipPipPipPip
  • 435 posts
  • Location:Edinburgh
  • Gender:Male

Posted 08 March 2007 - 08:01 PM

QUOTE(John @ Mar 8 2007, 07:35 PM) View Post
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. z>w has no meaning for w,z\in\mathbb{C}\setminus\mathbb{R}.
HSN contribute: Help the site grow!

Looking for a Maths tutor in West Lothian? Just PM me!

#7 John

    HSN Legend

  • Members
  • PipPipPipPipPipPipPipPip
  • 2,713 posts
  • Location:In a Peripheral Estate in Glasgow
  • Interests:First the boring stuff:<br /><br />2004 Results:<br /><br />Highers:<br /><br />Computing A<br />Craft and Design A<br />Physics A<br />Administration A<br />English A<br />Maths A<br />Modern Studies A<br />French A<br /><br />2005 Results:<br /><br />Advanced Highers:<br />Computing A<br />Physics A<br />Maths A<br />Modern Studies A<br />English A<br /><br />2006 Results:<br /><br />Advanced Highers(All Crashed):<br />Chemistry A<br />Biology A<br />Business Managemnt A<br /><br />Aren't I marvellous?
  • Gender:Male

Posted 08 March 2007 - 08:09 PM

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

#8 dfx

    Fully Fledged Genius

  • Members
  • PipPipPipPipPipPipPip
  • 1,955 posts
  • Gender:Male

Posted 09 March 2007 - 09:36 AM

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

Interesting. I'd say 'no'.


I shall agree. Thanks. smile.gif

#9 Sammie

    Top of the Class

  • Members
  • PipPipPipPipPip
  • 380 posts
  • Location:Glasgow
  • Interests:Stuff... mainly Fall Out Boy
  • Gender:Female

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
"Crowds are won and lost and won again, but our hearts beat for the diehards"

#10 Nathan

    Fully Fledged Genius

  • Members
  • PipPipPipPipPipPipPip
  • 1,736 posts
  • Location:Aberdeen, Scotland
  • Gender:Male

Posted 09 March 2007 - 06:52 PM

Congratulations smile.gif





1 user(s) are reading this topic

0 members, 1 guests, 0 anonymous users