If the slopes of the lines represented by K x | vedclass

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(C) The given equation is $K x^2 + 5 x y + y^2 = 0$.Comparing this with the general equation $a x^2 + 2 h x y + b y^2 = 0$,we have $a = K$,$2h = 5$,an

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$6$

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(C) The given equation is $K x^2 + 5 x y + y^2 = 0$.Comparing this with the general equation $a x^2 + 2 h x y + b y^2 = 0$,we have $a = K$,$2h = 5$,and $b = 1$.Let the slopes of the lines be $m_1$ and $m_2$.Then,$m_1 + m_2 = -\frac{2h}{b} = -5$ and $m_1 m_2 = \frac{a}{b} = K$.It is given that the difference between the slopes is $1$,i.e.,$|m_1 - m_2| = 1$.Using the identity $(m_1 - m_2)^2 = (m_1 + m_2)^2 - 4 m_1 m_2$,we substitute the values:$1^2 = (-5)^2 - 4(K)$.$1 = 25 - 4K$.$4K = 24$.$K = 6$.

If the slopes of the lines represented by $K x^2 + 5 x y + y^2 = 0$ differ by $1$,then $K =$

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