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
`therefore` Slope of another line is 2m.
We know that,
`m_(1)+m_(2)=-(2h)/(b) and m_(1)m_(2)=(a)/(b)`
`thereforem+2m=-(2h)/(b)`
`implies3m=(-2h)/(b)` . . . (i)
and `m(2m)=(a)/(b)`
`implies2m^(2)=(a)/(b)` . . . (ii)
On eliminating m, we get
`2((-2h)/(3b))^(2)=(a)/(b)`
`implies8h^(2)=9ab`