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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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The correct answer is:
$3 x^2-5 x y+2 y^2=0$
$2 x^2+5 x y+3 y^2=0 \Rightarrow(x+y)(2 x+3 y)=0$
lines are $x+y=0$ and $2 x+3 y=0$
so, perpendicular lines are $x-y=0$ and $3 x-2 y=0$
joint equation $(x-y)(3 x-2 y)=0$
$\Rightarrow 3 x^2-5 x y+2 y^2=0$
lines are $x+y=0$ and $2 x+3 y=0$
so, perpendicular lines are $x-y=0$ and $3 x-2 y=0$
joint equation $(x-y)(3 x-2 y)=0$
$\Rightarrow 3 x^2-5 x y+2 y^2=0$
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