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Question

(A) The given equation is $\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = \sqrt{3}$,

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${x^2} - {y^2} = 0$

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(A) The given equation is $\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = \sqrt{3}$,$h = -2$,and $b = \sqrt{3}$. The equation of the bisectors of the angles between the lines is given by $\frac{x^2 - y^2}{a - b} = \frac{xy}{h}$. Substituting the values,we get $\frac{x^2 - y^2}{\sqrt{3} - \sqrt{3}} = \frac{xy}{-2}$. Since the denominator on the left is $0$,the equation becomes $x^2 - y^2 = 0$.

The combined equation of the bisectors of the angle between the lines represented by $({x^2} + {y^2})\sqrt{3} = 4xy$ is

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