If the slope of one of the lines given by `ax^(2)+2hxy+by^(2)=0` is two times the other, then

Options

A. `8h^(2)-9ab`
B. `8h^(2)=9ab^(2)`
C. `8h=9ab`
D. `8h=9ab^(2)`

Answer

A

Explanation

We have, `ax^(2)+2hxy+by^(2)=0`
Let slope of one line is m
`:.` Slope of another line is 2 m
We know that,
`m_(1)+m_(2)=-(2h)/(b)`
and `m_(1)m_(2)=a/b`
`:.m+2m=-(2h)/(b)`
`rArr 3m=(-2h)/(b)` ...(i)
and `m(2m)=(a)/(b)`
`rArr 2m^(2)=a/b` ...(ii)
On eliminating m , we get
`2((-2h)/(3b))^(2)=a/b`
`rArr 8h^(2)=9ab`