The combined equation of the lines whose inclinations are $\frac{\pi}{6}$ and $\frac{5 \pi}{6}$, and passing…
The combined equation of the lines whose inclinations are $\frac{\pi}{6}$ and $\frac{5 \pi}{6}$, and passing through the origin, is
- $y^2-\sqrt{3} x^2=0$
- $3 x^2-y^2=0$
- $x^2-3 y^2=0$
- $\sqrt{3} y^2-x^2=0$
Solution
$\begin{aligned} & y=\tan \frac{\pi}{6} \cdot x \text { and } y=\tan \left(\frac{5 \pi}{6}\right) x \\ & \Rightarrow y=\frac{1}{\sqrt{3}} x \text { and } y=-\frac{1}{\sqrt{3}} x \\ & \Rightarrow x-\sqrt{3} y=0 \text { and } x+\sqrt{3} y=0 \\ & \text { combined equation }(x-\sqrt{3} y)(x+\sqrt{3} y)=0 \\ & \Rightarrow x^2-3 y^2=0\end{aligned}$
Asked in: MHT CET 2022 (10 Aug Shift 1)
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