Ellipse
Rational and Integral Points
Grade 11

Question:

<p>The number of rational points on the ellipse $\frac{x^2}{3} + y^2 = 1$ is ?</p>

Step-by-Step Solution

Key Concept: Ellipses with rational coefficients admit infinitely many rational points via parametric representation.
<p><strong>Step 1:</strong> Similar to the previous case, an ellipse with rational coefficients contains infinitely many rational points.</p><p><strong>Step 2:</strong> For $\frac{x^2}{3} + y^2 = 1$, parametric methods yield infinitely many rational solutions.</p><p>∴ Answer is $p$ (Infinite).</p>
Correct Answer: p

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