If the slopes of the lines $\mathrm{Kx}^2-4 \mathrm{xy}+5 \mathrm{y}^2=0$ differ by 2 , then $\mathrm{K}=$

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Aicharya · Accepted Answer

$\begin{aligned} & \left|m_1-m_2ight|=\sqrt{\left(m_1+m_2ight)^2-4 m_1 m_2}=\frac{2 \sqrt{h^2-a b}}{b} \ & \Rightarrow 2=\frac{2 \sqrt{(-2)^2-\mathrm{K} 	imes 5}}{5} \ & \Rightarrow 5=\sqrt{4-5 K} \ & \Rightarrow 25=4-5 \mathrm{~K} \ & \Rightarrow \mathrm{K}=\frac{-21}{5}\end{aligned}$

If the slopes of the lines $\mathrm{Kx}^2-4 \mathrm{xy}+5 \mathrm{y}^2=0$ differ by 2 , then $\mathrm{K}=$

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