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# What is the area of the region enclosed by lines y=x , x=-y,

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Manager
Joined: 10 May 2009
Posts: 60
What is the area of the region enclosed by lines y=x , x=-y, [#permalink]

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25 May 2009, 21:23
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What is the area of the region enclosed by lines y=x , x=-y, and the upper crescent of the circle y^2+x^2 =4?

Can someone please explain me the solution with a graph?

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Manager
Joined: 15 May 2009
Posts: 164

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25 May 2009, 21:43
1
prinits wrote:
What is the area of the region enclosed by lines y=x , x=-y, and the upper crescent of the circle y^2+x^2 =4?

Can someone please explain me the solution with a graph?

I'm not sure how to draw a graph & post it on the forum, but I think I got the problem, & hopefully I'm articulate enough to describe it.

y=x is a 45 degree diagonal line that passes through the I & III quadrants, as well as point (0,0);
y= -x is a line that is perpendicular to y=x, and intercepts that line at point (0,0);
y^2 + x^2 = 4 is a circle with a center at (0,0), and a radius of 2, so the area of the WHOLE circle is 2^2pi or 4pi.
The two aforementioned lines cuts through/encloses (however you want to say it) 50% of the upper half of the circle; in other words, 25% of the whole circle.
Therefore, the area of that enclosed region should be 4pi/4, or pi.
Manager
Joined: 10 May 2009
Posts: 60

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25 May 2009, 22:05
Got the point!! Thanks a lot
prinits wrote:
What is the area of the region enclosed by lines y=x , x=-y, and the upper crescent of the circle y^2+x^2 =4?

Can someone please explain me the solution with a graph?

I'm not sure how to draw a graph & post it on the forum, but I think I got the problem, & hopefully I'm articulate enough to describe it.

y=x is a 45 degree diagonal line that passes through the I & III quadrants, as well as point (0,0);
y= -x is a line that is perpendicular to y=x, and intercepts that line at point (0,0);
y^2 + x^2 = 4 is a circle with a center at (0,0), and a radius of 2, so the area of the WHOLE circle is 2^2pi or 4pi.
The two aforementioned lines cuts through/encloses (however you want to say it) 50% of the upper half of the circle; in other words, 25% of the whole circle.
Therefore, the area of that enclosed region should be 4pi/4, or pi.
Manager
Joined: 14 May 2009
Posts: 188

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25 May 2009, 23:08
See attached file

--== Message from GMAT Club Team ==--

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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File comment: Solution

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Re: M22 Q 20   [#permalink] 25 May 2009, 23:08
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