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In the xy-plane, C and D are circles centered at the origin
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29 Nov 2019, 02:35
29 Nov 2019, 02:35
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Question Stats:
61% (01:46) correct
38% (01:16) wrong based on 170 sessions
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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.
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.
Kudos for the right answer and explanation
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.
Kudos for the right answer and explanation
Re: In the xy-plane, C and D are circles centered at the origin
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29 Nov 2019, 18:33
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
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
General Discussion
Re: In the xy-plane, C and D are circles centered at the origin
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15 Feb 2020, 22:13
15 Feb 2020, 22:13
1
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?
