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Find the value of ‘k’, if the angle between the straight lines represented by $2 x^{2} + 5 x y + 3 y^{2} + 6 x + 7 y + 4 = 0$ is $\tan^{- 1} k$

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$\frac{1}{5}$ only

$\frac{- 1}{5}$ only

$\pm \frac{1}{5}$

answer is C.

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Detailed Solution

$\tan θ = 2 \frac{\sqrt{h^{2} - a b}}{| a + b |} = 2 \frac{\sqrt{{(\frac{5}{2})}^{2}} - 6}{5} = \pm \frac{1}{5}$
$θ = \tan^{- 1} (\pm \frac{1}{5}) s o k = \pm \frac{1}{5}$

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