If $4 x^2-5 x y+y^2=0$ represents a pair of lines with slopes $m_1$ and $m_2$, then the value of $\left|m_1-m_2\right|$ equals

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Aicharya · Accepted Answer

Given, equation of lines $ 4 x^2-5 x y+y^2=0 \Rightarrow y^2-5 x y+4 x^2=0 $ Here, $ 	ext { re, } \begin{aligned} m_1+m_2 & =5 \ m_1 m_2 & =4 \ \left(m_1-m_2ight)^2 & =\left(m_1+m_2ight)^2-4 m_1 m_2 \ \left(m_1-m_2ight)^2 & =(5)^2-4(4) \ \left|m_1-m_2ight| & =\sqrt{25-16}=3 \end{aligned} $

If $4 x^2-5 x y+y^2=0$ represents a pair of lines with slopes $m_1$ and $m_2$, then the value of…

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