The equation of the bisectors of the angle be | vedclass

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(A) The given equation is $(y - mx)^2 = (x + my)^2$.Expanding both sides,we get $y^2 + m^2x^2 - 2mxy = x^2 + m^2y^2 + 2mxy$.Rearranging the terms,we g

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$mx^2 + (m^2 - 1)xy - my^2 = 0$

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(A) The given equation is $(y - mx)^2 = (x + my)^2$.Expanding both sides,we get $y^2 + m^2x^2 - 2mxy = x^2 + m^2y^2 + 2mxy$.Rearranging the terms,we get $(m^2 - 1)x^2 - 4mxy + (1 - m^2)y^2 = 0$.This is of the form $Ax^2 + 2Hxy + By^2 = 0$,where $A = m^2 - 1$,$H = -2m$,and $B = 1 - m^2$.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 $\frac{x^2 - y^2}{(m^2 - 1) - (1 - m^2)} = \frac{xy}{-2m}$.$\frac{x^2 - y^2}{2(m^2 - 1)} = \frac{xy}{-2m}$.$-m(x^2 - y^2) = (m^2 - 1)xy$.$-mx^2 + my^2 = (m^2 - 1)xy$.$mx^2 + (m^2 - 1)xy - my^2 = 0$.

The equation of the bisectors of the angle between the lines represented by the equation $(y - mx)^2 = (x + my)^2$ is

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