If a line L is common to the pairs of lines 6 | vedclass

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(A) Solving the first pair of straight lines,we get: $6 x^2-x y-12 y^2=0$ $\Rightarrow 6 x^2-9 x y+8 x y-12 y^2=0$ $\Rightarrow 3 x(2 x-3 y)+4 y(2 x-3

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$10 x^2-19 x y+6 y^2=0$

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(A) Solving the first pair of straight lines,we get: $6 x^2-x y-12 y^2=0$ $\Rightarrow 6 x^2-9 x y+8 x y-12 y^2=0$ $\Rightarrow 3 x(2 x-3 y)+4 y(2 x-3 y)=0$ $\Rightarrow (3 x+4 y)(2 x-3 y)=0 \quad \dots (1)$ Solving the second pair of straight lines,we get: $15 x^2+14 x y-8 y^2=0$ $\Rightarrow 15 x^2+20 x y-6 x y-8 y^2=0$ $\Rightarrow 5 x(3 x+4 y)-2 y(3 x+4 y)=0$ $\Rightarrow (5 x-2 y)(3 x+4 y)=0 \quad \dots (2)$ From equations $(1)$ and $(2)$,we see that the line $3 x+4 y=0$ is common to both pairs. The other two lines are $2 x-3 y=0$ and $5 x-2 y=0$. The combined equation of these two lines is: $(2 x-3 y)(5 x-2 y)=0$ $\Rightarrow 10 x^2-4 x y-15 x y+6 y^2=0$ $\Rightarrow 10 x^2-19 x y+6 y^2=0$

If a line $L$ is common to the pairs of lines $6 x^2-x y-12 y^2=0$ and $15 x^2+14 x y-8 y^2=0$,then the combined equation of the other two lines is

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