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In the xy-plane, point (r, s) lies on a circle with center [#permalink]
 12 Apr 2005, 14:56
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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
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Last edited by Bunuel on 11 Feb 2012, 06:32, edited 2 times in total.
Edited the question and added the OA
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saurya_s 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 (v2, -v2) lies on the circle.
(1) r^2 + s^2 is the square of the radius of the circle. Sufficient.
(2) This is of no consequence since for any circle centered at the origin, there would be a point (v2. -v2) would lie on the circle. Gives us no info about r^2 + s^2.
Therefore, (A).
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DeeptiM wrote: OA is D...can anyone explain?? THEORY: In an xy-plane, 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. For more on this subject check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.htmlBACK 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. (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. Hope it helps.
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Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]
02 Mar 2013, 22:08
Thanks for the brilliant explanation. One thing I don't get the question is that, the point (r,s) could be anywhere in the circle, not only on its circumference. Why does it refer only to a point on the circumference? Thanks!
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Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]
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ryusei1989 wrote: Thanks for the brilliant explanation. One thing I don't get the question is that, the point (r,s) could be anywhere in the circle, not only on its circumference. Why does it refer only to a point on the circumference? Thanks! It is the language. On the circle = On the circumference. In/Inside/Within the circle = Points enclosed by the circumference
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In the XY-plane,point(r,s) [#permalink]
22 Apr 2013, 13:50
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})
Last edited by mun23 on 22 Apr 2013, 14:06, edited 1 time in total.
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Re: In the XY-plane,point(r,s) [#permalink]
22 Apr 2013, 13:55
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Re: In the XY-plane,point(r,s)
[#permalink]
22 Apr 2013, 13:55
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