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

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SVP
Joined: 29 Aug 2007
Posts: 2419
Q: A circle exists such that it touches both the y-axis and  [#permalink]

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03 Aug 2008, 23:08
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
Joined: 27 May 2008
Posts: 530
Re: Co-ordinate geometry  [#permalink]

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03 Aug 2008, 23:29
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
VP
Joined: 17 Jun 2008
Posts: 1279
Re: Co-ordinate geometry  [#permalink]

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05 Aug 2008, 19:07
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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cheers
Its Now Or Never

Re: Co-ordinate geometry &nbs [#permalink] 05 Aug 2008, 19:07
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# Q: A circle exists such that it touches both the y-axis and

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