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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?
A. 0
B. 2
C. 4
D. 6
E. 8
A. 0
B. 2
C. 4
D. 6
E. 8
04 Jan 2013, 05:53
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trex16864
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?
A. 0
B. 2
C. 4
D. 6
E. 8
A. 0
B. 2
C. 4
D. 6
E. 8
a^2+b^2=10 and a, b are integers means that 10 is the sum of two perfect squares.
10 is the sum of only one pair of perfect squares 1 and 9.
So, there can be 8 such points, 4 in each quadrant:
(1, 3);
(1, -3);
(-1, 3);
(-1, -3);
(3, 1);
(3, -1);
(-3, 1);
(-3, -1).
Answer: E.
04 Jan 2013, 07:47
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X and Y are integers and when squared have to equal 10. X and Y can take values of 1,3,-1,-3. The 1 and the 3 must be used in combination in order to add up to 10 (you cant use 1,1 or 3,3 or -1,-1, or -3,-3).
this leaves you with only 8 choices. answer E
this leaves you with only 8 choices. answer E
