Prove that the bisectors of the angle between the lines \( a x^{2}+...

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Prove that the bisectors of the angle between the lines \( a x^{2}+a c x y+c y^{2}=0 \) and \( \left(3+\frac{1}{c}\right) x^{2}+x y+\left(3+\frac{1}{a}\right) y^{2}=0 \) are always the same.
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