Home
Class 12
MATHS
The lines y = mx bisects the angle betwe...

The lines `y = mx` bisects the angle between the lines `ax^(2) +2hxy +by^(2) = 0` if

A

`h(1+m^(2)) = m(a+b)`

B

`h(1-m^(2))=m(a-b)`

C

`h(1+m^(2))=m(a-b)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of pair of bisectors of angles between lines `ax^(2) +2hxy +by^(2) =0` is
`(x^(2)-y^(2))/(xy) =(a-b)/(h)`
`rArr h(x^(2)-y^(2)) =(a-b) xy` (i)
But `y = mx` is one of these lines, then it will satisfy it. Substituting `y = mx` in (i)
`h(x^(2)-m^(2)x^(2)) =(a-b) x.mx`
Dividing by `x^(2)`, we get `h (1-m^(2)) =m(a-b)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the angle between the lines 3x^(2)-10xy-3y^(2)=0 :

Find the angle between the lines 3x^(2)+10xy+8y^(2)+14x+22+15=0

Show that the equation of the pair of lines bisecting the angles between the pair of bisectors of the angles between the pair of lines a x^2+2h x y+b y^2=0 is (a-b)(x^2-y^2)+4h x y=0.

The angle between the lines 2x - y+3 = 0 and x + 2y + 3 = 0 is

The angle between the lines x=1,y=2 and y=-1 ,z=0 is

The equation of the line which bisects the obtuse angle between the line x-2y+4=0 and 4x-3y+2=0 is

Find the equations of the bisector of the acute angle between the lines 3x + 4y + 2 = 0 and 5x + 12y - 5 = 0 .

The angle between the lines 2x+11y-7=0 and x + 3y + 5 = 0) is equal to

If h^(2)=ab then the angle between the pair of straight lines given by ax^(2)+2hxy+by^(2)=0 is