Let the line $y=m x$ and the ellipse $2 x^2+y^2=1$ intersect at a point $P$ in the first quadrant. If the normal to this ellipse at $P$ meets the co-ordinate axes at $\left(-\frac{1}{3 \sqrt{2}}, 0\right)$ and $(0, \beta)$, the $\beta$ is equal to
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