Question

If the line `y = mx` bisects the angle between the lines `ax^2 + 2h xy + by^2 = 0` then ` m ` is a root of the quadratic equation
A. `h(m^(2)-1)+m(b-1)=0`
B. `h(m^(2)-1)+m(a-b)`
C. `h(m^(2)+1)+m(a-b)=0`
D. none of these

Answer 1

Correct Answer - B
The combined equation of the bisectors of the angles between the lines given by `ax^(2)+2hxy+by^(2)=0` is
`(x^(2)-y^(2))/(a-b)=(xy)/(h)rArr hx^(2)-(a-b)xy-hy^(2)=0" …(i)"`
It is given that `y=mx` is one of the lines given by this equation.
Therefore,
`h-(a-b)m-hm^(2)=0" "["Putting y = mx in (i)"]`
`rArr" "h(m^(2)-1)+m(a-b)=0`