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# In the xy-plane, point (r, s) lies on a circle with center

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Manager
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In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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24 Aug 2010, 21:45
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:35) correct 31% (01:09) wrong based on 136 sessions

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In the xy-plane, point (r,s) lies on a circle with center at the origin. What is the value of $$r^2+s^2$$?

(1) The circle has radius 2.

(2) The point $$(sqrt{2}, -sqrt{2})$$ lies on the circle.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-xy-pl ... 65616.html
[Reveal] Spoiler: OA

Kudos [?]: 261 [0], given: 32

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Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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24 Aug 2010, 21:55
1
KUDOS
Equation of the circle is $$x^2+ y^2 = a^2$$ where a = radius

since r,s lies on the circle the equation becomes r^2+s^2 = a^2

statement 1: radius = $$a= 2 => r^2+s^2 = 2^2 = 4$$ , thus sufficient.
statement 2: we have given one point on the circle and we have the center at the origin.
Thus we can find out the distance between these 2 points which will be 2. This distance is basically the radius. Since we have the radius, the statement is sufficient.

Hence D
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Kudos [?]: 1927 [1], given: 235

Manager
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Kudos [?]: 261 [0], given: 32

Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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24 Aug 2010, 22:45
I had forgotten the equation for the circle. Thanks!

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Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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28 Aug 2010, 09:07
can some one please explain how B is correct ?
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Kudos [?]: 116 [0], given: 10

Manager
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Kudos [?]: 261 [0], given: 32

Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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28 Aug 2010, 10:06
Draw a right triangle from the origin to that point. Now solve for the hypotenuse, and you get 2. This is the radius of the circle.

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Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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09 Dec 2010, 09:31
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In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of r^2 + s^2?

(1) The circle has radius 2.
(2) The point ($$\sqrt{2}$$, $$-\sqrt{2}$$) lies on the circle.

Kudos [?]: 969 [0], given: 15

Math Expert
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Posts: 42605

Kudos [?]: 135629 [1], given: 12705

Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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09 Dec 2010, 09:45
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
udaymathapati wrote:
In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of
$$r^2 + s^2$$?
(1) The circle has radius 2.
(2) The point (\sqrt{$$2$$}, -\sqrt{$$2$$}) lies on the circle.

THEORY:
In an x-y Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that:
$$(x-a)^2+(y-b)^2=r^2$$

This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram above, the radius is the hypotenuse of a right-angled triangle whose other sides are of length x-a and y-b.

If the circle is centered at the origin (0, 0), then the equation simplifies to:
$$x^2+y^2=r^2$$

BACK TO THE ORIGINAL QUESTION:
In the xy-plane, point (r, s) lies on a circle with center at the origin. What is the value of $$r^2 + s^2$$?

Now, as $$x^2+y^2=r^2$$ then the question asks about the value of radius^2.

(2) The point $$(\sqrt{2}, \ -\sqrt{2})$$ lies on the circle --> substitute x and y coordinates of a point in $$x^2+y^2=r^2$$ --> $$2+2=4=r^2$$. Sufficient.

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Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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11 Aug 2015, 10:22
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Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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14 Aug 2017, 04:43
jpr200012 wrote:
In the xy-plane, point (r,s) lies on a circle with center at the origin. What is the value of $$r^2+s^2$$?

(1) The circle has radius 2.

(2) The point $$(sqrt{2}, -sqrt{2})$$ lies on the circle.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-the-xy-pl ... 65616.html
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Kudos [?]: 135629 [0], given: 12705

Re: In the xy-plane, point (r, s) lies on a circle with center   [#permalink] 14 Aug 2017, 04:43
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