The equation of the bisectors of angle between the lines represented by equation y - mx 2- x - my 2 isA- m x2-m2-1 x y-m y2-0B- m x2-m2-1 x y-m y2-0C- m x2-m2-1 x y-m y2-0D- None of these

The correct option is A The equation is nbsp; y^2 + m^2 x^2 2mxy x^2 m^2 y^2 2mxy = 0 ⇒ x^2(m^2 1) + y^2(1 m^2) 4mxy = 0 Therefore, the equati ...

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Standard XII

Mathematics

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Question

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

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None of these

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Solution

The correct option is A

The equation is

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

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

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

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

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

The correct option is A The equation is y2+m2x2−2mxy−x2−m2y2−2mxy=0 ⇒x2(m2−1)+y2(1−m2)−4mxy=0 Therefore, the equation of bisectors is x2−y2xy = (m2−1)−(1−m2)−2m⇒mx2+(m2−1)xy−my2=0.

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