The value of lambda such that lambda x^2-10 x | vedclass

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(C) The given equation is $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$. Comparing this with the general second-degree equation $a x^2+2 h x y+b y^2+2 g x+

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$2$

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(C) The given equation is $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$. Comparing this with the general second-degree equation $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$,we get: $a=\lambda, h=-5, b=12, g=\frac{5}{2}, f=-8, c=-3$. The condition for the equation to represent a pair of straight lines is $abc+2fgh-af^2-bg^2-ch^2=0$. Substituting the values: $\lambda(12)(-3) + 2(-8)(\frac{5}{2})(-5) - \lambda(-8)^2 - 12(\frac{5}{2})^2 - (-3)(-5)^2 = 0$. $-36\lambda + 200 - 64\lambda - 75 + 75 = 0$. $-100\lambda + 200 = 0$. $100\lambda = 200$. $\lambda = 2$.

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is:

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