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The line $y = 2 x + λ$ touches the hyperbola $16 x^{2} - 9 y^{2} = 144$ then $λ$ is

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$\pm 2 \sqrt{5}$

$\pm \sqrt{5}$

$\pm 3 \sqrt{5}$

$\pm 4 \sqrt{5}$

answer is A.

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Detailed Solution

$C^{2} = a^{2} m^{2} - b^{2} \Rightarrow λ^{2} = 9 (4) - 16 = 20 \Rightarrow λ = \pm 2 \sqrt{5}$

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