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Given the equation of the circle is x^2 + y^2 = 5^2 . How many points

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Bunuel
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Given the equation of the circle is x^2 + y^2 = 5^2 . How many points [#permalink] New post   22 Jul 2019, 00:11
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Given the equation of the circle is x^2 + y^2 = 5^2 . How many points on the circumference have both x and y coordinates integers ?

A. 6
B. 8
C. 10
D. 12
E. 14
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D
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Kinshook
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Given the equation of the circle is x^2 + y^2 = 5^2 . How many points [#permalink] New post   22 Jul 2019, 00:25
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Bunuel wrote:
Given the equation of the circle is x^2 + y^2 = 5^2 . How many points on the circumference have both x and y coordinates integers ?

A. 6
B. 8
C. 10
D. 12
E. 14



Given: the equation of the circle is x^2 + y^2 = 5^2 .
Asked: How many points on the circumference have both x and y coordinates integers ?

\(5^2 = 3^2 + 4^2 = 4^2+3^2 = 5^2 + 0^2 = 0^2 + 5^2 = 25\)

(3,4), (-3,4), (3,-4), (-3,-4), (4,3), (-4,3), (-4,3), (-4,-3), (0,5),(0,-5),(5,0),(-5,0) = 12 points with integer coordinates on the circumference.

IMO D
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Re: Given the equation of the circle is x^2 + y^2 = 5^2 . How many points [#permalink] New post   22 Jul 2019, 02:44
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The answer has to be D. only negative and positive values of 4 and 3 as well as 0 and 5 will answer our question.
This gives us 12 values namely:
-4,3|-3,4|,3,4|4,3|-4,-3|-3,-4|3,-4|4,-3|5,0|0,5|0,-5|-5,0|
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Re: Given the equation of the circle is x^2 + y^2 = 5^2 . How many points [#permalink] New post   22 Jul 2019, 10:16
Bunuel wrote:
Given the equation of the circle is x^2 + y^2 = 5^2 . How many points on the circumference have both x and y coordinates integers ?

A. 6
B. 8
C. 10
D. 12
E. 14


x^2 + y^2 = 5^2
we can have x,y as 3,4 which can be of +/- signs ; total 8 such pairs possible for each x & y 4 possible pairs possible and x & y can be interchanged; 4*2 ; 8 pairs
alongside (0,5) ( 5,0) ( 0,-5) & ( -5,0)
; 12 pairs possible
IMO D
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Re: Given the equation of the circle is x^2 + y^2 = 5^2 . How many points [#permalink] New post   30 Aug 2020, 05:35
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Re: Given the equation of the circle is x^2 + y^2 = 5^2 . How many points [#permalink]
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