Q111 / 170 · Manipal (MET) 2017 · Mathematics

If the angle between two lines represented by $2 x^2+5 x y+3 y^2+7 y+4=0$ is $\tan ^{-1} m$, then $m$ is equal to

Correct answer
A
$1 / 5$
B
$1$
C
$7 / 5$
D
7

Solution

$\begin{gathered} \text { Here, } a=2, b=3, h=\frac{5}{2} \\ \therefore \tan \theta=\frac{2 \sqrt{\left(\frac{5}{2}\right)^2-6}}{2+3} \\ \Rightarrow m=\frac{1}{5}\end{gathered}$

Hence, the correct answer is option: 'A'.

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