In the xy-plane, point (r, s) lies on a circle with center : Quant Question Archive [LOCKED]
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# In the xy-plane, point (r, s) lies on a circle with center

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Director
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06 Feb 2006, 16:51
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of
r2 + s2?
(1) The circle has radius 2.
(2) The point (sqrt2, -sqrt2) lies on the circle.
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06 Feb 2006, 17:35
joemama142000 wrote:
In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of
r2 + s2?
(1) The circle has radius 2.
(2) The point (sqrt2, -sqrt2) lies on the circle.

D. since r2 + s2 is redius^2 and both give the value of redius^2.
Director
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07 Feb 2006, 05:32
D, agree with prof's expln.
Senior Manager
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08 Feb 2006, 22:15
D both enough independently..
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09 Feb 2006, 00:42

(1) Sufficient. We know the radius, so we know r^2 + s^2 = 4

(2) Sufficient. Using the values, r^2 + s^2 = (sqrt(2))^2 + (-sqrt(2))^2 = 4

Ans D
Manager
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09 Feb 2006, 07:06
Can someone help explain this in a little more detail?
Ther must be some property of circles that I am not familiar with...
SVP
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09 Feb 2006, 07:18
kook44 wrote:
Can someone help explain this in a little more detail?
Ther must be some property of circles that I am not familiar with...

friend, the key fact of this problem is that the distance from the centre of a circle to any point on the circle is equal to the radius of the circle. Here, the centre is the origin of the coordination plane thus:
the distance from the centre to the provided point =
sqrt [ (r-0)^2 + (s-0)^2] = sqrt (r^2 + s^2)
this distance= the radius ---> sqrt(r^2+s^2) = 2 ---> r^2+s^2= 4

---> stmt 1 is suff

stmt 2 already provides us the measure of the radius ---> back to stmt 1 ---> suff
Manager
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09 Feb 2006, 07:31
Ah-
I think I was interpreting the question wrong. It says:
joemama142000 wrote:
In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of
r2 + s2?
(1) The circle has radius 2.
(2) The point (sqrt2, -sqrt2) lies on the circle.

I guess they are supposed to be r^2 + s^2?
Director
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10 Feb 2006, 02:36
it is supposed to be r^2 and s^2. If it were not, then the problem would be very deceptive. Sorry if i caused any confusion.
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11 Feb 2006, 03:41
laxieqv wrote:
kook44 wrote:
Can someone help explain this in a little more detail?
Ther must be some property of circles that I am not familiar with...

friend, the key fact of this problem is that the distance from the centre of a circle to any point on the circle is equal to the radius of the circle. Here, the centre is the origin of the coordination plane thus:
the distance from the centre to the provided point =
sqrt [ (r-0)^2 + (s-0)^2] = sqrt (r^2 + s^2)
this distance= the radius ---> sqrt(r^2+s^2) = 2 ---> r^2+s^2= 4

---> stmt 1 is suff

stmt 2 already provides us the measure of the radius ---> back to stmt 1 ---> suff

thnk u , i cld ve picked A , but now i understand.
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11 Feb 2006, 03:41
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