Find the value of k, if the angle between the straight lines represented by 2x2 + 5xy + 3y2 + 6x + 7y + 4 = 0 is Tan-1(k)

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Find the value of k, if the angle between the straight lines represented by 2x² + 5xy + 3y² + 6x + 7y + 4 = 0 is Tan^-1(k)

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(1/5) only

(-1/5) only

$\pm$ 1/5

answer is C.

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Detailed Solution

Let $θ$ be the angle between given pair of lines
Now $θ = {Tan}^{- 1} k \Rightarrow k = \tan θ = \frac{2 \sqrt{h^{2} - ab}}{| a + b |} = \frac{2 \sqrt{25 / 4 - (2) (3}}{| 2 + 3 |}$
$= \frac{1}{| 5 |} \Rightarrow k = \pm \frac{1}{5}$

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