If the slope of one of the lines represented by `ax^2+2hxy+by^2=0` is the sqaure of the other , then

Options

A. `a^2b+ab^2-6abh+8h^3=0`
B. `a^2b+ab^2+6abh+8h^3=0`
C. `a^2b+ab^2-3abh+8h^3=0`
D. `a^2b+ab^2-6abh-8h^3=0`

Answer

A

Explanation

We have , `ax^2+2hxy+by^2=0` ....(i)
Let `m_1=m`
Then , `m_2=m^2`
From Eq.(i) , we get `m_1+m_2=(-2h)/(b)rArr m+m^2=(-2h)/(b)` .....(ii)
and `m_1.m_2=(a)/(b)rArr m.m^2=(a)/(b)`
`rArr m^3=(a)/(b)`
Cubing both sides of Eq. (ii), we get `(m+m^2)^3=(-8h^3)/(b^3)`
`rArr m^3+m^6+3m^3(m+m^2)=(-8h^3)/(b^3)`
`rArr (a)/(b)+((a)/(b))^2+(3a)/(b)((-2h)/(b))=(-8h^3)/(b^3)`
`rArr (a)/(b)+(a^2)/(b^2)-(6ah)/(b^2)=(-8h^3)/(b^3)`
`rArr (ab+a^2-6ah)/(b^2)=(-8h^3)/(b^3)`
`rArr b(ab+a^2-6ah)=-8h^3`
`rArr ab^2+a^2b-6abh+8h^3=0`