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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XI

Mathematics

Family of straight lines

The equation ...

Question

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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 $\frac{x^{2} - y^{2}}{x y}$

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

Suggest Corrections

Similar questions

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

Q. If one of the lines of

m y^{2} + (1 - m^{2}) x y - m x^{2} = 0

is a bisector of the angle between the lines xy=0, then m=

Q. If one of the line of

{m y}^{2} + ({1 - m}^{2}) x y - {m x}^{2} = 0

is a bisector of the angle between the lines xy = 0, then m is

Q. If one of the lines of is

m y^{2} + (1 - m^{2}) x y - m x^{2} = 0

is a bisector of the angle between the lines

x y = 0,

then

m

The coordinates of the point R which divides the line segment joining two points P (x₁, y₁, z₁) and Q (x₂, y₂, z₂) externally in the ratio m : n are given by

Join BYJU'S Learning Program

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