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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 (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.

In the xy-plane, point (r, s) lies on a circle with center [#permalink]
11 Feb 2012, 05:30

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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: \(x^2+y^2=r^2\).

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 \(x^2+y^2=radius^2\) 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 \(x^2+y^2=radius^2\) --> \(2+2=4=r^2\). Sufficient.

Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]
02 Mar 2013, 21:08

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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!

Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]
02 Mar 2013, 23:02

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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 _________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well." ― Voltaire Press Kudos, if I have helped. Thanks! shit-happens-my-journey-to-172475.html#p1372807

Re: In the xy-plane, point (r, s) lies on a circle with center [#permalink]
05 Jul 2014, 01:53

Hello from the GMAT Club BumpBot!

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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 (2√, −2√) lies on the circle

You seem to have misunderstood a little here.

The equation of Circle is given by \(x^2 + y^2 = Radius^2\)

Given : (r,s) lie on the circle i.e. (r,s) will satisfy the equation of Circle i.e. \(r^2 + s^2 = Radius^2\)

Question : Find the value of \(r^2 + s^2\)? but since \(r^2 + s^2 = Radius^2\) therefore, the question becomes

Question : Find the value of \(Radius^2\)?

Statement 1: The circle has radius 2 i.e. \(r^2 + s^2 = Radius^2 = 2^2 = 4\) SUFFICIENT

Statement 2: The point (√2, −√2) lies on the circle i.e. (√2, −√2) will satisfy the equation of circle i.e. (√2)^2 + (−√2)^2 = Radius^2 i.e. Radius = 4 hence, \(r^2 + s^2 = Radius^2 = 2^2 = 4\) Hence, SUFFICIENT

Answer: Option D

I hope it helps!

Please Note: You have been confused r (X-co-ordinate) and r (Radius) as it seems from your question _________________