If the lines $x^2-4 x y+y^2=0$ make angles $\alpha$ and $\beta$ with positive direction of X-axis, then $\cot ^2 \alpha+\cot ^2 \beta=$

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Aicharya · Accepted Answer

We have lines $x^2-4 x y+y^2=0$ and slopes of the lines are $	an \alpha$ and $	an \beta$. $\begin{aligned} & 	herefore 	an \alpha+	an \beta=4 	ext { and } 	an \alpha \cdot 	an \beta=1 \ & 	herefore 	an \alpha=\frac{1}{	an \beta}=\cot \beta \ & 	herefore \cot \beta+	an \beta=4 	ext { squaring we get } \cot ^2 \beta+	an ^2 \beta+2=16 \ & \Rightarrow 	an ^2 \beta+\cot ^2 \beta=14 \end{aligned}$

If the lines $x^2-4 x y+y^2=0$ make angles $\alpha$ and $\beta$ with positive direction of X-axis, then…

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