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Circle & rectangular coordinate system

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Circle & rectangular coordinate system

by crackgmat007 » Fri May 08, 2009 12:00 pm
Q: In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the
maximum possible value of the radius of C ?
A. 2
B. 4
C. 8
D. 16
E. There is no finite maximum value.

How to arrive at 16?
Last edited by crackgmat007 on Fri May 29, 2009 7:24 am, edited 1 time in total.
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Re: Circle & rectangular coordinate system

by Ian Stewart » Fri May 08, 2009 2:29 pm
crackgmat007 wrote:Q: In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the
maximum possible value of the radius of C ?
A. 2
B. 4
C. 8
D. 16
E. There is no finite maximum value.

How to arrive at 16?
Well, if you do arrive at 16, you're not getting the correct answer. The radius here can be as large as you want. For example, take the point (0,100) as the center of the circle. The two points (4,0) and (-4,0) are the same distance from (0,100), so we can certainly draw a circle with center (0,100) that passes through those two points. The radius of that circle is going to be a bit more than 100 (you can find it exactly by solving for r in r^2 = 100^2 + 4^2, though we don't need to do that here). So the answer is E.
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by sgdravid » Fri May 29, 2009 1:49 am
I am not able to understand the explanation. If the centree of circle is 0,100, how can draw a circle which passes thru' 4,0 and -4,0.


I think the maximum radius is 4, (the line connecting 4,0 and -4,0 is the diameter)

Please correct me if I am wrong
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by acemans » Wed Aug 18, 2010 9:42 am
any point eqi-distant from both the points can be the center or the circle so there are infinite points that satisfy the equation

the y axis being one set of points. (0,x) where x= real numbers

so E is the answer :)
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