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REPEATER 2024 — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsREPEATER 20242 Marks
Question
Find the acute angle between the lines represented by $x y+y^2=0$.
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Answer

Comparing $x y+y^2$ with $a x^2+2 h x y+b y^2=0$, we get,
$a=0,2 h=1, b=1$
$\begin{array}{ll}\therefore & \theta=\tan ^{-1}\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right| \\
\therefore & \theta=\tan ^{-1}\left|\frac{2 \sqrt{\left(\frac{1}{2}\right)^2-0}}{0+1}\right|=\tan ^{-1}\left|2 \sqrt{\frac{1}{4}}\right|=\tan ^{-1}\left|\frac{2}{2}\right| \\ \therefore & \theta=\tan ^{-1}|1| \\
\therefore & \theta=\frac{\pi}{4}\end{array}$
Thus, the acute angle between the lines is $\frac{\pi}{4}$.

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