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In the xy-plane, C and D are circles centered at the origin

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In the xy-plane, C and D are circles centered at the origin [#permalink] New post   29 Nov 2019, 02:35
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In the xy-plane, \(C\) and \(D\) are circles centered at the origin with radii \(\sqrt{17}\) and \(\sqrt{5}\), respectively.


Quantity A
Quantity B
The number of points (a, b) on circle \(C\) where both a and b are integers
The number of points (a, b) on circle \(D\) where both a and b are integers




A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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Re: In the xy-plane, C and D are circles centered at the origin [#permalink] New post   29 Nov 2019, 18:33
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Equation of circle C: x2 + y2 = 17
Equation of circle D: x2 + y2 = 5

The question can now be rephrased as: number of integer pairs of (x,y) that satisfy above equations
For circle C, you have (4,1) and its 3 other variants by interchanging the -ve sign - (4,1),(4,-1),(-4,1),(-4,-1). Similar pattern of roots by interchanging x & y. - 4 more i.e. (1,4),(1,-4),(-1,4),(-1,-4)
For circle D, as well 8 roots obtained by interchanging signs & positions of (2,1)

Thus option C
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Re: In the xy-plane, C and D are circles centered at the origin [#permalink] New post   15 Feb 2020, 22:13
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Correct me if I am wrong but if I try to plot the Two CIRCLES ( Centred @ Origin & given their Radii's ) aren't they concentric and The Bigger Circle C will have more Integer Points Inside it than the Circle D. Or am i missing something here?
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Re: In the xy-plane, C and D are circles centered at the origin [#permalink] New post   16 Feb 2020, 06:21
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Yiddo_Bhushan wrote:
Correct me if I am wrong but if I try to plot the Two CIRCLES ( Centred @ Origin & given their Radii's ) aren't they concentric and The Bigger Circle C will have more Integer Points Inside it than the Circle D. Or am i missing something here?


You're thinking about the number of integer points INSIDE the circle, but the question asks for integer points ON the circle.
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Re: In the xy-plane, C and D are circles centered at the origin [#permalink] New post   14 Aug 2022, 22:10
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We have to remember that a,b are integer that are actually two sides of right triangle since circles are from origin. How can we create the right triangles where hypotenuses are square root 5 and 17. Am I thinking wrong? For that square root of two triangles all together 4 and 4 i.e 1,2 and -1-2, 2-1, 1-2.

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Re: In the xy-plane, C and D are circles centered at the origin [#permalink] New post   21 Aug 2022, 00:05
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Number of Integer points on the circle means as C and D are concentric circles the value will be the same for both .
Hence , Answer is C.
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Re: In the xy-plane, C and D are circles centered at the origin [#permalink] New post   07 Oct 2023, 20:52
Hello from the GRE Prep Club BumpBot!

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Re: In the xy-plane, C and D are circles centered at the origin [#permalink]
07 Oct 2023, 20:52
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