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artshep
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Point (a, b) is on the circle represented by x^2 + y^2 = 10, 14 Nov 2006, 18:43
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Point (a, b) is on the circle represented by x^2 + y^2 = 10, and a, b are integers. How many such points are possible?

I count 12 points, however, the answer given is 8.

My logic:
Any combination where the x and y coordinates are both/each less than or equal to ten and the sum of the squares of those coordinates equals 100.

So, I counted the following points:
(0,10), (10,0), (-10, 0), (0, -10), (8,6), (6,8), (-6, -8), (-8, -6), (8, -6), (6, -8), (-8, 6), (-6, 8)

Any idea what's wrong here?

Artis



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enola
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Point (a, b) is on the circle represented by x^2 + y^2 = 10, 14 Nov 2006, 18:57
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I think the key here is that the circle equation is x^2 + y^ 2 = r^2. So if x^2 + y^2 = 10 that means r = sqrt 10. So we need to find combination of integers a and b such that a^2 + b^2 = 10.

I reason that since the circle started at the center, to find the total possible points, i only need to look at the first quadrant, and times 4. In the first quadrant, only (1,3) and (3,1) satisfy the condition. This means there are a total of 4*2 = 8 points.
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artshep
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Point (a, b) is on the circle represented by x^2 + y^2 = 10, 14 Nov 2006, 19:14
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Oh, geez. Silly mistake. I took the radius to be 10 instead of SQRT(10). Thanks for letting me know.

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