The combined equation of the pair of lines through the origin and perpendicular to the pair of lines given by `ax^(2)+2hxy+by^(2)=0`, is

Options

A. `ax^2-2hxy+by^2=0`
B. `bx^2+2hxy+ay^2=0`
C. `bx^2-2hxy+ay^2=0`
D. `bx^2+2hxy-ay^2=0`

Answer

C

Explanation

Let `y=m_1x and y=m_2x` be the lines represented by `ax^2+2hxy+by^2=0`. Then ,
`m_1+m_2=-(2h)/(b) and m_1m_2=(a)/(b)` .....(i)
The equations of the lines passing through the origin and perpendicular to `y=m_1x and y=m_2x` respectively are `m_1y+x=1 and m_2y+x=0`
The combined equation of these lines is
`(m_1y+x)(m_2y+x)=0`
`rArr m_1m_2y^2+xy(m_1+m_2)+x^2=0`
`rArr (a)/(b)y^2-(2h)/(b)xy+x^2=0`
`therefore ay^2-2hxy +bx^2=0`