Question

If the line y=mx bisects the angle between the lines ax^2+2hxy+by^2=0 then m is a root of the quadratic equation

Answer 1

hx^2+(a−b)x−h=0

Equation of bisectors of the pair of straight lines ax^2+2hxy+by^2=0 is

h(x^2−y^2)−(a−b)xy=0==>>(1)

Since y=mx is given to be the bisector of the pair of straight lines, then the line will satisfy the equation (1)

Then we get,

h(1−m^2)−(a−b)m=0

hm^2+(a−b)m−h=0

So m satisfies the equation

hx^2 +(a−b)x−h=0.