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

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Intern
Joined: 07 Jun 2017
Posts: 18

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

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

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.

(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.

Hope it helps.

Excellent! Thanks!

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Kudos [?]: 0 [0], given: 14

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

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