Let a line \( L: 2 x+y=k, k0 \) be a tangent to the hyperbola \( x^...

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Let a line \( L: 2 x+y=k, k0 \) be a tangent to the hyperbola \( x^{2}-y^{2}=3 \). If \( L \) is also a tangent to the parabola
\( \mathrm{P} \) \( y^{2}=\alpha x \), then \( \alpha \) is equal to:
[JEE Main-2021 (July)]
(a) 12
(b) \( -12 \)
(c) 24
(d) \( -24 \)
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