Question

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

• A. $mx^{2} + (m^{2} - 1)xy - my^{2} = 0$
• B. $mx^{2} - (m^{2} - 1)xy - my^{2} = 0$
• C. $mx^{2} + (m^{2} - 1)xy + my^{2} = 0$
• D. None of these

Answer 1

Answer: (A)

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

Answer 2

The equation is

$y^{2} + m^{2}x^{2} - 2mxy - x^{2} - m^{2}y^{2} - 2mxy = 0$

$\Rightarrow x^{2}(m^{2} - 1) + y^{2}(1 - m^{2}) - 4mxy = 0$

Therefore, the equation of bisectors is $\frac{x^{2} - y^{2}}{xy}$

$= \frac{(m^{2} - 1) - (1 - m^{2})}{- 2m} \Rightarrow mx^{2} + (m^{2} - 1)xy - my^{2} = 0$.