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

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

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New post 24 Aug 2010, 21:45
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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

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

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New post 24 Aug 2010, 21:55
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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 xy-plane, point (r, s) lies on a circle with center [#permalink]

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New post 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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New post 28 Aug 2010, 09:07
can some one please explain how B is correct ?
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Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]

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

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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:
\((x-a)^2+(y-b)^2=r^2\)


Image

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.

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

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

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New post 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
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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