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 $ y^{2}=\alpha x $, then $ \alpha $ is equal to: [JEE Main 2021, 22 Jul (Shift 2)]

Question

Let a line $ L: 2 x+y=k, k>0 $ be a tangent to the hyperbola $ x^{2}-y^{2}=3 $. If $ L $ is also a tangent to the parabola $ y^{2}=\alpha x $, then $ \alpha $ is equal to: [JEE Main 2021, 22 Jul (Shift 2)]

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