The number of points with positive integral coordinates satisfying $f(x,y) > 0, g(x,y) 3$ and $x < 6$ is:
Step-by-Step Solution
Key Concept: Lattice point enumeration requires checking which integer coordinates satisfy all three constraints simultaneously.
Points satisfying the given conditions must lie within circle $f(x,y) = 0$, above the line $y = 3$, and below the line $y = 2$. The valid lattice points are: $(1,5), (1,6), (2,5), (2,6), (3,5), (3,6), (4,5), (4,6), (5,4), (5,5), (5,6)$. These points represent integer coordinate pairs in the region bounded by the circle and the specified horizontal lines.
Correct Answer: 4