<p>The number of integral points on the ellipse $\frac{x^2}{3} + y^2 = 1$ is ?</p>
Step-by-Step Solution
Key Concept: Check integer coordinates within the bounds defined by the ellipse equation and verify which satisfy the equation exactly.
<p><strong>Step 1:</strong> For the ellipse $\frac{x^2}{3} + y^2 = 1$, we need $x^2 \leq 3$ and $y^2 \leq 1$.</p><p><strong>Step 2:</strong> Integer values: $x \in \{-1, 0, 1\}$ and $y \in \{-1, 0, 1\}$.</p><p><strong>Step 3:</strong> Check $(0, \pm 1)$: $0 + 1 = 1$ ✓; $(\pm 1, 0)$: $\frac{1}{3} + 0 \neq 1$ ✗.</p><p><strong>Step 4:</strong> Only integral points are $(0, 1)$ and $(0, -1)$.</p><p><strong>Step 5:</strong> Total = 2.</p><p>∴ Answer is $r$ (2).</p>
Correct Answer: r