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(B) The given equation is $2 x^2+5 x y+3 y^2=0$. Factorizing the equation: $2 x^2+2 x y+3 x y+3 y^2=0$ $\Rightarrow 2 x(x+y)+3 y(x+y)=0$ $\Rightarrow

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$3 x^2-5 x y+2 y^2=0$

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(B) The given equation is $2 x^2+5 x y+3 y^2=0$. Factorizing the equation: $2 x^2+2 x y+3 x y+3 y^2=0$ $\Rightarrow 2 x(x+y)+3 y(x+y)=0$ $\Rightarrow (2 x+3 y)(x+y)=0$. The individual lines are $2 x+3 y=0$ and $x+y=0$. The lines perpendicular to these lines and passing through the origin are $3 x-2 y=0$ and $x-y=0$. The joint equation is $(3 x-2 y)(x-y)=0$. Expanding this,we get $3 x^2-3 x y-2 x y+2 y^2=0$,which simplifies to $3 x^2-5 x y+2 y^2=0$.

The joint equation of two lines passing through the origin and perpendicular to the lines given by $2 x^2+5 x y+3 y^2=0$ is

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