1.

(p,q) is called a lattice point if p and q are both integers . How many lattice points lie in the area strictly between the two curves x^(2) + y^(2) = 9 and x^(2) + y^(2) - 6x + 5 = 0 ?

Answer»

0
1
2
3

Solution :Plot the graphs of `y = pm sqrt(9 - x^(2)) ` and `y = pm sqrt(-x^2 + 6x - 5)` in the STANDARD WINDOW , but with FORMAT set to Grid On. The "grid" CONSISTS exactly of the lattice points .
ZOOM/Z Box around the area enclosed by the two graphs , and count the number of lattice points in that area to be 3 . The points (1,0) and (3,0) appear close to the boundary , but a mental check finds that (1,0) is on the boundary of the second curve , while (3,0) is on the boundary of the first .


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