How do you prove that two circles just touch each other?
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Circle
Started by SomethingTypical, Dec 07 2004 08:01 PM
14 replies to this topic
#2
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Posted 07 December 2004 - 08:02 PM
well if they touch each other then the 2 equation equal eac other at that point
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#3
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Posted 07 December 2004 - 08:04 PM
QUOTE(Dave @ Dec 7 2004, 09:02 PM)
well if they touch each other then the 2 equation equal eac other at that point
Makes sense, thanks.
#4
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Posted 08 December 2004 - 04:15 PM
Ah, I remember that! I actually keep up to date on the higher by helping a friend who does higher at the moment.
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Posted 08 December 2004 - 06:50 PM
hey. its to do with the radius of the 2 circles maybe? find the centres nd then do sum stuff! lol- sorry im so vague- reely in a rush!!
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Posted 08 December 2004 - 09:51 PM
I did it by:
If the sum of the two radii = the distance from one center to another, then they touch at one point.
If the sum of the two radii > the distance from one center to another, then they touch at two points.
If the sum of the two radii < the distance from one center to another, then they don't touch.
If the sum of the two radii = the distance from one center to another, then they touch at one point.
If the sum of the two radii > the distance from one center to another, then they touch at two points.
If the sum of the two radii < the distance from one center to another, then they don't touch.
#7
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Posted 08 December 2004 - 10:10 PM
That is infact how you do it, remember if the distance isnt just a horizontal or vertical line you can form a sort of right-angeld triangle between the two centres with distance (d) as the hypotenuse and use pythagoras to calculate it.
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#8
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Posted 09 December 2004 - 05:41 PM
I'd use the distance formula. Eg. if one circle (arbitrarily) had equation (x-4)^2 + (y+1)^2 = 25 and the other (also arbitrarily) (x+1)^2 + (y-1)^2 = 16 then I'd find the center of both circles using (-g, -f) -> (-1, 1) and (4, -1). Use distance formula, the compare this with the sum of the radii (will be 9 here).
#9
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Posted 10 December 2004 - 02:15 PM
[B][I][FONT=Times][SIZE=7][COLOR=purple]Actually I think it’s the right answer to this question 
#12
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Posted 27 January 2006 - 10:36 AM
Hi, just a quick question... when you are asked to write down the equation of a circle in the exam, can you leave it in the form (x-a)^2+(y-b)^2=r^2, or do you have to expland the brackets?
Thanks
Thanks
#13
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Posted 27 January 2006 - 11:37 AM
QUOTE(Amo @ Jan 27 2006, 10:36 AM)
Hi, just a quick question... when you are asked to write down the equation of a circle in the exam, can you leave it in the form (x-a)^2+(y-b)^2=r^2, or do you have to expland the brackets?
Thanks
Thanks
I think it's fine as it is.
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#14
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Posted 28 January 2006 - 03:59 PM
QUOTE(Amo @ Jan 27 2006, 10:36 AM)
Hi, just a quick question... when you are asked to write down the equation of a circle in the exam, can you leave it in the form (x-a)^2+(y-b)^2=r^2, or do you have to expland the brackets?
Thanks
Thanks
You only need to expand the brackets if the question asks you to give the equation of the circle in expanded form.
#15
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Posted 28 January 2006 - 06:53 PM
Ok thanks! 
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