if coordinate axes are the angle bisectors of the pair of lines `ax^2+2hxy+by^2 =0` then

Options

A. `a+b=0`
B. `h=0`
C. `h ne 0, a+b=0`
D. `a+b ne 0`

Answer

B

Explanation

The combined equation of the angle bisectors of lines given by `ax^(2)+2hxy+by^(2)=0`, is
`(x^(2)-y^(2))/(a-b)=(xy)/(h)`
`rArr" "(a-b)xy=(x^(2)-y^(2))h" …(i)"`
It is given that the coordinate axes are the bisectors of the angles between the lines given by `ax^(2)+2hxy+by^(2)=0`. So, their combined equation is
`xy=0" ...(ii)"`
From (i) and (ii), we get `h=0, a-b ne0`