If the slope of one of the lines given by K x | vedclass

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(C) The given equation of the pair of lines is $K x^2 + 6 x y + y^2 = 0$. Comparing this with the general form $A x^2 + 2 H x y + B y^2 = 0$,we get $A

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$\frac{27}{4}$

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(C) The given equation of the pair of lines is $K x^2 + 6 x y + y^2 = 0$. Comparing this with the general form $A x^2 + 2 H x y + B y^2 = 0$,we get $A = K$,$H = 3$,and $B = 1$. Let the slopes of the two lines be $m_1$ and $m_2$. We know that $m_1 + m_2 = \frac{-2 H}{B} = -6$ and $m_1 m_2 = \frac{A}{B} = K$. Given that one slope is three times the other,let $m_2 = 3 m_1$. Substituting this into the sum of slopes: $m_1 + 3 m_1 = -6$ $\Rightarrow 4 m_1 = -6$ $\Rightarrow m_1 = -\frac{3}{2}$. Now,using the product of slopes: $m_1 	imes (3 m_1) = K \Rightarrow 3 m_1^2 = K$. Substituting $m_1 = -\frac{3}{2}$: $K = 3 	imes (-\frac{3}{2})^2 = 3 	imes \frac{9}{4} = \frac{27}{4}$.

If the slope of one of the lines given by $K x^2 + 6 x y + y^2 = 0$ is three times the other,then the value of $K$ is:

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