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Q: A circle exists such that it touches both the y-axis and

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SVP
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Joined: 29 Aug 2007
Posts: 2470

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Q: A circle exists such that it touches both the y-axis and [#permalink]

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New post 03 Aug 2008, 22:08
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Q: A circle exists such that it touches both the y-axis and the line with equation x=y. What is the y-coordinate of the center of the circle ?

1. The x-coordinate of the center of the circle is 1.
2. The area of the circle is pi.
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Director
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Joined: 27 May 2008
Posts: 540

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Re: Co-ordinate geometry [#permalink]

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New post 03 Aug 2008, 22:29
GMAT TIGER wrote:
Q: A circle exists such that it touches both the y-axis and the line with equation x=y. What is the y-coordinate of the center of the circle ?

1. The x-coordinate of the center of the circle is 1.
2. The area of the circle is pi.



good problem, refer this 7-t16826

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VP
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Re: Co-ordinate geometry [#permalink]

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New post 05 Aug 2008, 18:07
GMAT TIGER wrote:
Q: A circle exists such that it touches both the y-axis and the line with equation x=y. What is the y-coordinate of the center of the circle ?

1. The x-coordinate of the center of the circle is 1.
2. The area of the circle is pi.


Draw the circle in graph touching x=y and y axis.
equation 0f the circle is :
say x1,y1 is center :
(x-x1)^2 +(y-y1)^2=x1^2
X1 is the radius of this circle since it touches y axis.

(1) x1=1 => (x-1)^2 +(y-y1)^2=1 => x=y =>
(y-1)^2 +(y-y1)^2=1 => not solvable y1 depends on y
INSUFFI
(2)area =pi means radius =1 => x1=1 => (y-1)^2 +(y-y1)^2=1 =>? INSUFFI

Combining both (1) and (2),both give x1=1 =>INSUFFI as seen above
Hence IMO E
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Kudos [?]: 434 [0], given: 0

Re: Co-ordinate geometry   [#permalink] 05 Aug 2008, 18:07
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