If the slope of one line in the pair `ax^(2)+4xy+y^(2)=0` is three times the other, then a =

Options

A. 1
B. 2
C. 3
D. 4

Answer

C

Explanation

We have , `ax^2+4xy+y^2=0` ....(i)
and `m_1=3m_2` .....(ii)
From Eq.(i) , we get `m_1+m_2=(-4)/(1)`.......(iii)
and `m_1.m_2=(a)/(1)`......(iv)
`rArr 3m_2.m_2=a`
`rArr 3m_(2)^(2)=a`
`rArr m_(2)^(2)=(a)/(3)` ....(v)
From Eqs. (ii) and (iii), we get `3m_(2)+m_2=-4`
`rArr 4m_(2)=-4`
`rArr m_2=-1` ....(vi)
Using Eq.(vi) in Eq.(v), we get `(-1)^2=(a)/(3)`
`rArr a=3`.