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MathNet 2004 — Part 01 Question 183

Math Olympiad Vault · MathNet 2004 — Part 01

Question 183

Assume that $M = \{(x, y) \mid x^2 + 2y^2 = 3\}$, and $N = \{(x, y) \mid y = mx + b\}$. If $M \cap N \neq \emptyset$ for all $m \in \mathbb{R}$, then $b$ takes values from ( ).
  1. $\left[-\frac{\sqrt{6}}{2}, \frac{\sqrt{6}}{2}\right]$
  2. $\left(-\frac{\sqrt{6}}{2}, \frac{\sqrt{6}}{2}\right)$
  3. $\left(-\frac{\sqrt{6}}{2}, \frac{\sqrt{6}}{2}\right]$
  4. $\left[-\frac{2\sqrt{3}}{3}, \frac{2\sqrt{3}}{3}\right]$