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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Aicharya · Accepted Answer

Straight lines $2 x^2+5 x y+3 y^2+6 x+7 y+4=0$ Angle between straight lines represented by $\begin{aligned} & a x^2+b y^2+2 g x+2 f y+c+2 h x y=0 \text { is } \ & \tan \theta=\frac{2 \sqrt{h^2-a b}}{a+b} \end{aligned}$ $\begin{aligned} \tan \theta & =\frac{2 \sqrt{(5 / 2)^2-6}}{5}= \pm \frac{1}{5} \ \Rightarrow \quad \theta & =\tan ^{-1} K=\tan ^{-1}\left( \pm \frac{1}{5}\right) \Rightarrow\left(K= \pm \frac{1}{5}\right) \end{aligned}$

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…

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