<p>The number of integral points on the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$ is ?</p>
Step-by-Step Solution
Key Concept: Systematically check integer values within the domain to find all integral points on the ellipse.
<p><strong>Step 1:</strong> An integral point has both coordinates as integers.</p><p><strong>Step 2:</strong> For the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$, substitute integer values of $x \in \{-3, -2, -1, 0, 1, 2, 3\}$.</p><p><strong>Step 3:</strong> Check: $(0, 2)$, $(0, -2)$, $(3, 0)$, $(-3, 0)$ satisfy the equation.</p><p><strong>Step 4:</strong> Verify other integers: $(\pm 1, y)$ or $(\pm 2, y)$ do not yield integer $y$ values.</p><p><strong>Step 5:</strong> Total integral points = 4.</p><p>∴ Answer is $q$ (4).</p>
Correct Answer: q