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In the xyplane, point (r, s) lies on a circle with center [#permalink]
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24 Aug 2010, 22:45
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In the xyplane, 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: inthexyplanepointrsliesonacirclewithcentera165616.html== Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost 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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Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
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24 Aug 2010, 22:55
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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Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
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24 Aug 2010, 23:45
I had forgotten the equation for the circle. Thanks!



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Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
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28 Aug 2010, 10:07
can some one please explain how B is correct ?
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Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
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28 Aug 2010, 11:06
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 xyplane, point (r, s) lies on a circle with center [#permalink]
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09 Dec 2010, 10:31
In the xyplane, 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.



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Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
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09 Dec 2010, 10:45
udaymathapati wrote: In the xyplane, 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 xy Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that: \((xa)^2+(yb)^2=r^2\) 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 rightangled triangle whose other sides are of length xa and yb. 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 xyplane, 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. (1) The circle has radius 2 > radius^2=4. Sufficient. (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. Answer: D.
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Re: In the xyplane, point (r, s) lies on a circle with center [#permalink]
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14 Aug 2017, 05:43




Re: In the xyplane, point (r, s) lies on a circle with center
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