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

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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 06 Sep 2017, 07:21
Bunuel wrote:
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:
\((x-a)^2+(y-b)^2=r^2\)


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

For more on this subject check Coordinate Geometry chapter of Math Book: http://gmatclub.com/forum/math-coordina ... 87652.html

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.

Answer: D.

Hope it helps.


Excellent! Thanks!

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Re: In the xy-plane, point (r, s) lies on a circle with center   [#permalink] 06 Sep 2017, 07:21

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