Let a line \( L_{1} \) be tangent to the hyperbola \( P \) \( \frac...

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Let a line \( L_{1} \) be tangent to the hyperbola
\( P \) \( \frac{x^{2}}{16}-\frac{y^{2}}{4}=1 \) and let \( L_{2} \) be the line passing through

W. the origin and perpendicular to \( L_{1} \). If the locus of the point of intersection of \( L_{1} \) and \( L_{2} \) is \( \left(x^{2}+y^{2}\right)^{2}=\alpha x^{2}+ \) \( \beta y^{2} \), then \( \alpha+\beta \) is equal to
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