The equation $k x^{2} + 4 x y + 5 y^{2} = 0$ represents two lines inclined at an angle $π$ if $k$ is

\frac{5}{4}

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\frac{4}{5}

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- \frac{4}{5}

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none of these

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Solution

The correct option is B $\frac{4}{5}$
$tan θ = \frac{2 \sqrt{h^{2} - a b}}{a + b}$
$\Rightarrow 0 = \frac{2 \sqrt{2^{2} - 5 k}}{k + 5}$
$\Rightarrow 2 \sqrt{2^{2} - 5 k} = 0$
$\Rightarrow k = \frac{4}{5}$

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